The real deal on DOGE – Double pan and handle LTC and USD

Get DOGE today. A pan and handle is forming on Doge in terms of LTC and USD over different periods of time. The next couple weeks will tell, but if DOGE outperforms these two over the next couple weeks, look for a massive surge in Doge price.
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https://coinreport.net/cryptsy-debitway-partner-foster-altcoin-trading/

 

News like THIS does not hurt either. With the alt coin market gaining traction for trading more regularly and with more liquidity, I’m gunna go ahead and say that DOGE is a buy.

The risk that doge will decrease is substantial, but with Bitcoin’s bouncing of the 266 low, you could look for stability there, and gain faith in the entire alt coin market.

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You will want to read the following for starters on understanding \ bitcoin cryptography.

 

  Some Bitcoin for Thought


You will want to read the following for starters on understanding bitcoin \
cryptography.
https : // en.bitcoin.it/wiki/Secp256k1
http : // en.wikisource.org/wiki/NIST_Koblitz _Curves _Parameters
The naive way to break an encryption algorithm is to brute –
force the key.The complexity of that attack is 2 n,
where n is the key length.All cryptanalytic attacks can be viewed as \
shortcuts to that method.And since the efficacy of a brute –
force attack is a direct function of key length,
these attacks effectively shorten the key.So if, for example,
the best attack against DES has a complexity of 239,
that effectively shortens DES⎟ s 56 –
bit key by 17 bits.That⎟ s a really good attack, by the way.Right now the \
upper practical limit on brute force is somewhere under 80 bits.However, \
using that as a guide gives us some indication as to how good an attack has \
to be to break any of the modern algorithms.These days, encryption algorithms \
have, at a minimum, 128 –
bit keys.That means any NSA cryptoanalytic breakthrough has to reduce the \
effective key length by at least 48 bits in order to be practical.
http : // en.wikipedia.org/wiki/Elliptic_Curve _DSA
http : //
www.reddit.com/r/Bitcoin/comments/1 nvsn7/
elliptic_curve _secp256k1 _vulnerability/
http : // blog.ezyang.com/2011/06/the – cryptography – of – bitcoin/
http : //
bitcoinmagazine.com/6021/bitcoin – is – not – quantum – safe – and – how –
we – can – fix/
http : // en.wikipedia.org/wiki/Cryptographic_hash _function
http : // mathworld.wolfram.com/EllipticCurve.html
We can liken the finding of bitcoins to someone firing at a target, and they \
are force to fire at the target while wearing a blind fold.

We can make the statistical probability of hitting the target greater if we \
either

1. Take off the blind fold (very hard)
2. Make the target bigger (easier)
3. Create a net so that we hit the target and drag it back to us so that it’ \
s easier to hit.
Making target bigger :
Say we know what the elliptical curve that bitcoin uses, we can can create \
more facets to it.
We can embed different functions within it; reduce it to other variable \
entirely.
Then, we have better ways of converting to potential solutions to the \
equation.
We need to know what the field characteristic of the bitcoin elliptical curve \
is.
http : //
bitcoin.stackexchange.com/questions/21907/what – does – the – curve – used –
in – bitcoin – secp256k1 – look – like
http : // www.secg.org/index.php?action = secg, docs_secg
Actually secp256k1 is defined over a Galois field, not a ring of integers \
modulo a prime.Now, it turns out that the secp256k1 field is a prime field \
and therefore isomorphic to a ring of integers modulo a prime, but this is \
not true for all ECDSA curves– in fact, the “sectXXXyZ” curves (for which \
much faster hardware exists than the “secpXXXyZ” curves) cannot be described \
using rings of integers.See this page for an explanation of why every finite \
field has a GF representation but only the prime fields have a a Z/
pZ representation :

en.wikipedia.org/wiki/Finite_field # Statement
See : Fp2 (via quadratic residues modulo p) –
Not wholly true. Not necessarily correct.
Here, phenomenological velocity can be used.
Please research what is the relationship between Fp2 and bitcoin secp256k1?
http : //
www.reddit.com/r/Bitcoin/comments/1 nvsn7/
elliptic_curve _secp256k1 _vulnerability/
“On their protocol specification wiki they say that in their scripts they \
provide hexidecimal decompressed x,y coordinates (though these are really r,s \
values)”
So, if x and y are actually r and s, then we can boil either down to only one \
variable. We can actually force r to be purely in terms of s by definition.
But what are r and s?
http : //
bitcoinmagazine.com/7781/satoshis – genius – unexpected – ways – in – which –
bitcoin – dodged – some – cryptographic – bullet/
Thus, elliptic curve cryptography uses an elliptic curve with two \
modifications.First,
the equation is now y2 =
x3 + ax + b +
kp, where k can be any integer and p is some large prime number (a \
parameter of the curve alongside a and b).Second, x and y must be \
integers.Although the resulting set is hardly a ⎥curve⎠, surprisingly enough \
the same math still works, and the restriction to integers avoids rounding \
errors.
y^2 = x^3 + ax + b + kp
In general, however, the curves fall into two categories :
⎥pseudorandom⎠ curves and Koblitz curves.In a pseudorandom curve, the \
parameters a and b are chosen by a specified algorithm (essentially a hash) \
from a certain ⎥seed⎠.For secp256r1,
the standard 256 –
bit pseudorandom curve, the seed is \
c49d360886e704936a6678e1139d26b7819f7e90, giving rise to the parameters :
Vitalik Buterin : Fortunately, Bitcoin does not use pseudorandom curves;
Bitcoin uses Koblitz curves.In Bitcoin⎟ s secp256k1, the parameters are :
p = 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
a = 0
b = 7

y^2 == x^3 + 0 x + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
This is the base equation for bitcoin elliptical curves from what Vitalik \
says, and Vitalik is the top notch #1 programmer in the bizzz.                \
\

Theta BASE
y = height of cone = h = Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π)
x = base of cone = Sqrt[(r^2 – η^2)] = (2 π r – r θ)/(2 π)
y^2 == x^3 + 0 x + 7 +
k 1157920892373161954235709850086879078532699846656405640394575840079088346\
71663 =

(Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2 == ((2 π r – r θ)/(2 π))^3 +
0 (2 π r – r θ)/(2 π) + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 1157920892373161954235709850086879078532699846656405640394575840079088346\
71663 k + (2 π r – r θ)^3/(8 π^3)
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3), r]
{{r -> (2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) + (4 2^(
1/3) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3)) + (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413253317\
30501069312 k π^9 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239759951\
91503207936 k π^8 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549699939\
89379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033133293\
26252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887424984\
97344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774849969\
9468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145708308\
289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132\
5331730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397\
5995191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496\
9993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331\
3329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874\
2498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748\
499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457\
08308289079208 k π^3 θ^6)^2))^(
1/3)/(3 2^(1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))}, {r -> (
2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 + I Sqrt[3]) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ +
6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(
1/3)) – ((1 – I Sqrt[3]) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3))/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))}, {r -> (
2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 – I Sqrt[3]) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ +
6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(
1/3)) – ((1 + I Sqrt[3]) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3))/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))}}
But what is zero? Is it really so nothing?
Usefulness : 0 = 2 π r – 2 π x – θ r
0 = 2 π r – 2 π x – θ r
So, let’ s try that again :
(Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2 == ((2 π r – r θ)/(2 π))^3 +
0 (2 π r – r θ)/(2 π) + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3), r]
(Sqrt[4 π r^2 θ – r^2 θ^2]/(
2 π))^2 == ((2 π r – r θ)/(2 π))^3 + (2 π r – 2 π x – θ r) (2 π r – r θ)/(
2 π) + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 1157920892373161954235709850086879078532699846656405640394575840079088346\
71663 k + (2 π r – r θ)^3/(8 π^3) + ((2 π r – r θ) (2 π r – 2 π x – r θ))/(
2 π)
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3) + ((2 π r – r θ) (2 π r – 2 π x – r θ))/(
2 π), r]
{{r -> -((2 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))) – (2^(
1/3) (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3)))/(3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 –
30720 π^10 θ^2 – 20736 π^8 x θ^2 – 69120 π^9 x θ^2 +
242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3))^3))^(1/3)) +
1/(3 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413253317\
30501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239759951\
91503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549699939\
89379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033133293\
26252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887424984\
97344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774849969\
9468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145708308\
289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132\
5331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397\
5995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496\
9993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331\
3329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874\
2498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748\
499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457\
08308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))^3))^(
1/3)}, {r -> -((2 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3))) + ((1 +
I Sqrt[3]) (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)))/(3 2^(
2/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 –
30720 π^10 θ^2 – 20736 π^8 x θ^2 – 69120 π^9 x θ^2 +
242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3))^3))^(1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 – I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))^3))^(
1/3)}, {r -> -((2 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3))) + ((1 –
I Sqrt[3]) (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)))/(3 2^(
2/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 –
30720 π^10 θ^2 – 20736 π^8 x θ^2 – 69120 π^9 x θ^2 +
242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3))^3))^(1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 + I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6 +
,((-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 – 8192 π^12 – 18432 π^11 x + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ + 12288 π^10 θ + 24576 π^11 θ + 9216 π^9 x θ +
55296 π^10 x θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 – 6144 π^8 θ^2 – 27648 π^9 θ^2 – 30720 π^10 θ^2 –
20736 π^8 x θ^2 – 69120 π^9 x θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 + 9216 π^7 θ^3 + 24576 π^8 θ^3 + 20480 π^9 θ^3 +
18432 π^7 x θ^3 + 46080 π^8 x θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 – 4992 π^6 θ^4 – 10752 π^7 θ^4 – 7680 π^8 θ^4 –
8064 π^6 x θ^4 – 17280 π^7 x θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 + 1152 π^5 θ^5 + 2304 π^6 θ^5 + 1536 π^7 θ^5 +
1728 π^5 x θ^5 + 3456 π^6 x θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6 – 96 π^4 θ^6 – 192 π^5 θ^6 – 128 π^6 θ^6 –
144 π^4 x θ^6 – 288 π^5 x θ^6)^2 +
4 (-4 (8 π^4 – 4 π^2 θ – 8 π^3 θ + π θ^2 + 2 π^2 θ^2)^2 –
24 (2 π^4 x – π^3 x θ) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3))^3))^(
1/3)}}
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3) + ((2 π r – r θ) (2 π r – 2 π x – r θ))/(
2 π), k]
{{k -> (-56 π^3 – 16 π^4 r^2 – 8 π^3 r^3 + 16 π^4 r x + 8 π^2 r^2 θ +
16 π^3 r^2 θ + 12 π^2 r^3 θ – 8 π^3 r x θ – 2 π r^2 θ^2 –
4 π^2 r^2 θ^2 – 6 π r^3 θ^2 +
r^3 \
θ^3)/(926336713898529563388567880069503262826159877325124512315660672063270677\
373304 π^3)}}
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3) + ((2 π r – r θ) (2 π r – 2 π x – r θ))/(
2 π), k]
{{k -> (-56 π^3 – 16 π^4 r^2 – 8 π^3 r^3 + 16 π^4 r x + 8 π^2 r^2 θ +
16 π^3 r^2 θ + 12 π^2 r^3 θ – 8 π^3 r x θ – 2 π r^2 θ^2 –
4 π^2 r^2 θ^2 – 6 π r^3 θ^2 +
r^3 \
θ^3)/(926336713898529563388567880069503262826159877325124512315660672063270677\
373304 π^3)}}
c := 2.99792458*(10^8)
Solve[(Sqrt[r Sqrt[1 – (v)^2/c^2]] Sqrt[θ/Sqrt[1 – (v)^2/c^2]] Sqrt[
4 π r – r θ])/(2 π) == r Sin[β], v]
{{v -> -((
1. Sqrt[-1.12941*10^18 θ + 8.98755*10^16 θ^2 + 3.54814*10^18 Sin[β]^2])/
Sqrt[-12.5664 θ + θ^2 + 39.4784 Sin[β]^2])}, {v ->
Sqrt[-1.12941*10^18 θ + 8.98755*10^16 θ^2 + 3.54814*10^18 Sin[β]^2]/
Sqrt[-12.5664 θ + θ^2 + 39.4784 Sin[β]^2]}}
Solve[(4 π r^2 θ – r^2 θ^2)/(4 π^2) ==
7 + 115792089237316195423570985008687907853269984665640564039457584007908834\
671663 k + (2 π r – r θ)^3/(8 π^3) + ((2 π r – r θ) (2 π r – 2 π x – r θ))/(
2 π), k]
(Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2 == ((2 π r – r θ)/(2 π))^3 +
0 (2 π r – r θ)/(2 π) + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
0 = (2 π r – 2 π x – θ r) =
0 = θ r – (2 π r – 2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)]) =
0
(Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2 == ((2 π r – r θ)/(2 π))^3 +
0 (2 π r – r θ)/(2 π) + 7 +
k 11579208923731619542357098500868790785326998466564056403945758400790883467\
1663
θ r – (2 π r – 2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)])
Solve[(Sqrt[4 π r^2 θ – r^2 θ^2]/(
2 π))^2 == ((2 π r – r θ)/(
2 π))^3 + (θ r – (2 π r –
2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)])) (
2 π r – r θ)/(2 π) + 7 +
k 1157920892373161954235709850086879078532699846656405640394575840079088346\
71663, k]
{{k -> (-56 π^3 + 16 π^4 r^2 – 8 π^3 r^3 – 8 π^3 r Sqrt[r^2 (2 π – θ)^2] +
8 π^2 r^2 θ – 16 π^3 r^2 θ + 12 π^2 r^3 θ +
4 π^2 r Sqrt[r^2 (2 π – θ)^2] θ – 2 π r^2 θ^2 + 4 π^2 r^2 θ^2 –
6 π r^3 θ^2 +
r^3 \
θ^3)/(926336713898529563388567880069503262826159877325124512315660672063270677\
373304 π^3)}}
Solve[(Sqrt[4 π r^2 θ – r^2 θ^2]/(
2 π))^2 == ((2 π r – r θ)/(
2 π))^3 + (θ r – (2 π r –
2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)])) (
2 π r – r θ)/(2 π) + 7 +
k 1157920892373161954235709850086879078532699846656405640394575840079088346\
71663, r]
{{r -> (2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) + (4 2^(
1/3) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ + 6 π θ^2 –
θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3)) +
1/(3 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413253317\
30501069312 k π^9 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239759951\
91503207936 k π^8 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549699939\
89379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033133293\
26252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887424984\
97344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774849969\
9468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145708308\
289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132\
5331730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397\
5995191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496\
9993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331\
3329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874\
2498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748\
499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457\
08308289079208 k π^3 θ^6)^2))^(1/3)}, {r -> (2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 + I Sqrt[3]) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ +
6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 – I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6)^2))^(1/3)}, {r -> (2 (4 π^2 θ – π θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 – I Sqrt[3]) (4 π^2 θ – π θ^2)^2)/(3 (8 π^3 – 12 π^2 θ +
6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6)^2))^(1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 + I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 +
,(-256 (4 π^2 θ – π θ^2)^6 + (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 + 18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 – 1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6)^2))^(1/3)}, {r -> (
2 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 + 4 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) + (4 2^(
1/3) (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 + 4 π^2 θ^2)^2)/(3 (8 π^3 –
12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 –
163840 π^9 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)) +
1/(3 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413253317\
30501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239759951\
91503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549699939\
89379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033133293\
26252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887424984\
97344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774849969\
9468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145708308\
289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132\
5331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397\
5995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496\
9993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331\
3329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –

150066547651561789268947996571259528577837900126670170995137028874\
2498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748\
499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457\
08308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)}, {r -> (2 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 + 4 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 + I Sqrt[3]) (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^2)/(3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 –
163840 π^9 θ^3 – 91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 – I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 –
163840 π^9 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)}, {r -> (2 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 + 4 π^2 θ^2))/(
3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) – (2 2^(
1/3) (1 – I Sqrt[3]) (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^2)/(3 (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3) (-96768 π^9 –
160070984161665908553544529676010163816360426801781515728146164132533\
1730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
480212952484997725660633589028030491449081280405344547184438492397599\
5191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
600266190606247157075791986285038114311351600506680683980548115496999\
3989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
400177460404164771383861324190025409540901067004453789320365410331332\
9326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
150066547651561789268947996571259528577837900126670170995137028874249\
8497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
300133095303123578537895993142519057155675800253340341990274057748499\
699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
250110912752602982114913327618765880963063166877783618325228381457083\
08289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641\
325331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923\
975995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154\
969993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103\
313329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 –
163840 π^9 θ^3 – 91488 π^5 θ^4 –

1500665476515617892689479965712595285778379001266701709951370288\
742498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577\
48499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814\
5708308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)) –
1/(6 2^(
1/3) (8 π^3 – 12 π^2 θ + 6 π θ^2 – θ^3)) (1 + I Sqrt[3]) (-96768 π^9 –
1600709841616659085535445296760101638163604268017815157281461641325331\
730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +
4802129524849977256606335890280304914490812804053445471844384923975995\
191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
6002661906062471570757919862850381143113516005066806839805481154969993\
989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 + 245760 π^10 θ^2 +
242944 π^6 θ^3 +
4001774604041647713838613241900254095409010670044537893203654103313329\
326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 – 163840 π^9 θ^3 –
91488 π^5 θ^4 –
1500665476515617892689479965712595285778379001266701709951370288742498\
497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
3001330953031235785378959931425190571556758002533403419902740577484996\
99468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
2501109127526029821149133276187658809630631668777836183252283814570830\
8289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6 +
,(-256 (16 π^4 + 4 π^2 θ – 16 π^3 θ – π θ^2 +
4 π^2 θ^2)^6 + (-96768 π^9 –
16007098416166590855354452967601016381636042680178151572814616413\
25331730501069312 k π^9 + 65536 π^12 + 290304 π^8 θ +

48021295248499772566063358902803049144908128040534454718443849239\
75995191503207936 k π^8 θ + 49152 π^10 θ – 196608 π^11 θ – 362880 π^7 θ^2 –
60026619060624715707579198628503811431135160050668068398054811549\
69993989379009920 k π^7 θ^2 + 12288 π^8 θ^2 – 110592 π^9 θ^2 +
245760 π^10 θ^2 + 242944 π^6 θ^3 +
40017746040416477138386132419002540954090106700445378932036541033\
13329326252673280 k π^6 θ^3 – 18432 π^7 θ^3 + 98304 π^8 θ^3 –
163840 π^9 θ^3 – 91488 π^5 θ^4 –
15006654765156178926894799657125952857783790012667017099513702887\
42498497344752480 k π^5 θ^4 + 9984 π^6 θ^4 – 43008 π^7 θ^4 + 61440 π^8 θ^4 +
18336 π^4 θ^5 +
30013309530312357853789599314251905715567580025334034199027405774\
8499699468950496 k π^4 θ^5 – 2304 π^5 θ^5 + 9216 π^6 θ^5 – 12288 π^7 θ^5 –
1528 π^3 θ^6 –
25011091275260298211491332761876588096306316687778361832522838145\
708308289079208 k π^3 θ^6 + 192 π^4 θ^6 – 768 π^5 θ^6 + 1024 π^6 θ^6)^2))^(
1/3)}}
Solve[(2 π (2 π r – 2 π Sqrt[r^2 – (η)^2]))/θ^2 == (4 π r^2 – 2 r^2 θ)/(
2 Sqrt[4 π r^2 θ – r^2 θ^2]), r]
0 = (2 π (2 π r – 2 π Sqrt[r^2 – (η)^2]))/θ^2 – (4 π r^2 – 2 r^2 θ)/(
2 Sqrt[4 π r^2 θ – r^2 θ^2]) = 0
Solve[(2 π (2 π r – 2 π Sqrt[r^2 – (η)^2]))/θ^2 – (4 π r^2 – 2 r^2 θ)/(
2 Sqrt[
4 π r^2 θ – r^2 θ^2]) == (θ r – (2 π r – 2 π Sqrt[(r^2 – η^2)])) + (1 –
Sqrt[4 π θ – θ^2]/(2 π Sin[β])), r]
{{}}
Solve[(2 π (2 π r – 2 π Sqrt[r^2 – (η)^2]))/θ^2 – (4 π r^2 – 2 r^2 θ)/(
2 Sqrt[
4 π r^2 θ –
r^2 θ^2]) == (θ r – (2 π r –
2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)])) + (1 – Sqrt[
4 π θ – θ^2]/(2 π Sin[β])), η]
{{η -> -1/(
32 π^3) (,(512 π^4 r θ^2 – 1024 π^5 r^2 θ^2 +
512 π^4 r Sqrt[r^2 (2 π – θ)^2] θ^2 – 64 π^3 r^2 θ^3 +
512 π^4 r^2 θ^3 – 64 π^2 θ^4 + 256 π^3 r θ^4 + 48 π^2 r^2 θ^4 –
512 π^4 r^2 θ^4 – 128 π^2 Sqrt[r^2 (2 π – θ)^2] θ^4 +
256 π^3 r Sqrt[r^2 (2 π – θ)^2] θ^4 – 128 π^2 r θ^5 – 4 π r^2 θ^5 +
512 π^3 r^2 θ^5 – 128 π^2 r Sqrt[r^2 (2 π – θ)^2] θ^5 – r^2 θ^6 –
128 π^2 r^2 θ^6 – (r^2 θ^7)/(4 π – θ) +
256 π^4 r θ Sqrt[r^2 (4 π – θ) θ] –
64 π^3 r θ^2 Sqrt[r^2 (4 π – θ) θ] –
64 π^2 θ^3 Sqrt[r^2 (4 π – θ) θ] –
16 π^2 r θ^3 Sqrt[r^2 (4 π – θ) θ] +
128 π^3 r θ^3 Sqrt[r^2 (4 π – θ) θ] –
64 π^2 Sqrt[r^2 (2 π – θ)^2] θ^3 Sqrt[r^2 (4 π – θ) θ] +
16 π θ^4 Sqrt[r^2 (4 π – θ) θ] – 4 π r θ^4 Sqrt[r^2 (4 π – θ) θ] –
96 π^2 r θ^4 Sqrt[r^2 (4 π – θ) θ] +
16 π Sqrt[r^2 (2 π – θ)^2] θ^4 Sqrt[r^2 (4 π – θ) θ] +
4 θ^5 Sqrt[r^2 (4 π – θ) θ] – r θ^5 Sqrt[r^2 (4 π – θ) θ] +
8 π r θ^5 Sqrt[r^2 (4 π – θ) θ] +
4 Sqrt[r^2 (2 π – θ)^2] θ^5 Sqrt[r^2 (4 π – θ) θ] +
2 r θ^6 Sqrt[r^2 (4 π – θ) θ] + (4 θ^6 Sqrt[r^2 (4 π – θ) θ])/(
4 π – θ) – (r θ^6 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) + (
4 Sqrt[r^2 (2 π – θ)^2] θ^6 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) + (
2 r θ^7 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) –
256 π^3 r θ^2 Sqrt[(4 π – θ) θ] Csc[β] +
64 π θ^4 Sqrt[(4 π – θ) θ] Csc[β] –
128 π^2 r θ^4 Sqrt[(4 π – θ) θ] Csc[β] +
64 π Sqrt[r^2 (2 π – θ)^2] θ^4 Sqrt[(4 π – θ) θ] Csc[β] +
64 π r θ^5 Sqrt[(4 π – θ) θ] Csc[β] +
32 π θ^3 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β] –
8 θ^4 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β] – (
8 θ^5 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β])/(4 π – θ) –
64 π θ^5 Csc[β]^2 + 16 θ^6 Csc[β]^2))}, {η ->
1/(32 π^3) (,(512 π^4 r θ^2 – 1024 π^5 r^2 θ^2 +
512 π^4 r Sqrt[r^2 (2 π – θ)^2] θ^2 – 64 π^3 r^2 θ^3 +
512 π^4 r^2 θ^3 – 64 π^2 θ^4 + 256 π^3 r θ^4 + 48 π^2 r^2 θ^4 –
512 π^4 r^2 θ^4 – 128 π^2 Sqrt[r^2 (2 π – θ)^2] θ^4 +
256 π^3 r Sqrt[r^2 (2 π – θ)^2] θ^4 – 128 π^2 r θ^5 – 4 π r^2 θ^5 +
512 π^3 r^2 θ^5 – 128 π^2 r Sqrt[r^2 (2 π – θ)^2] θ^5 – r^2 θ^6 –
128 π^2 r^2 θ^6 – (r^2 θ^7)/(4 π – θ) +
256 π^4 r θ Sqrt[r^2 (4 π – θ) θ] –
64 π^3 r θ^2 Sqrt[r^2 (4 π – θ) θ] –
64 π^2 θ^3 Sqrt[r^2 (4 π – θ) θ] –
16 π^2 r θ^3 Sqrt[r^2 (4 π – θ) θ] +
128 π^3 r θ^3 Sqrt[r^2 (4 π – θ) θ] –
64 π^2 Sqrt[r^2 (2 π – θ)^2] θ^3 Sqrt[r^2 (4 π – θ) θ] +
16 π θ^4 Sqrt[r^2 (4 π – θ) θ] – 4 π r θ^4 Sqrt[r^2 (4 π – θ) θ] –
96 π^2 r θ^4 Sqrt[r^2 (4 π – θ) θ] +
16 π Sqrt[r^2 (2 π – θ)^2] θ^4 Sqrt[r^2 (4 π – θ) θ] +
4 θ^5 Sqrt[r^2 (4 π – θ) θ] – r θ^5 Sqrt[r^2 (4 π – θ) θ] +
8 π r θ^5 Sqrt[r^2 (4 π – θ) θ] +
4 Sqrt[r^2 (2 π – θ)^2] θ^5 Sqrt[r^2 (4 π – θ) θ] +
2 r θ^6 Sqrt[r^2 (4 π – θ) θ] + (4 θ^6 Sqrt[r^2 (4 π – θ) θ])/(
4 π – θ) – (r θ^6 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) + (
4 Sqrt[r^2 (2 π – θ)^2] θ^6 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) + (
2 r θ^7 Sqrt[r^2 (4 π – θ) θ])/(4 π – θ) –
256 π^3 r θ^2 Sqrt[(4 π – θ) θ] Csc[β] +
64 π θ^4 Sqrt[(4 π – θ) θ] Csc[β] –
128 π^2 r θ^4 Sqrt[(4 π – θ) θ] Csc[β] +
64 π Sqrt[r^2 (2 π – θ)^2] θ^4 Sqrt[(4 π – θ) θ] Csc[β] +
64 π r θ^5 Sqrt[(4 π – θ) θ] Csc[β] +
32 π θ^3 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β] –
8 θ^4 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β] – (
8 θ^5 Sqrt[(4 π – θ) θ] Sqrt[r^2 (4 π – θ) θ] Csc[β])/(4 π – θ) –
64 π θ^5 Csc[β]^2 + 16 θ^6 Csc[β]^2))}}

Solve[1 – Sqrt[4 π θ – θ^2]/(2 π Sin[β]) ==
θ r – (2 π r – 2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)]), r]
Solve[1 – (2 π Sin[β])/Sqrt[4 π θ – θ^2] ==
θ r – (2 π r – 2 π Sqrt[(r^2 – (Sqrt[4 π r^2 θ – r^2 θ^2]/(2 π))^2)]), r]

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Bitcoin Fat Finger Part Deux

http://www.reddit.com/r/Bitcoin/comments/2ib5hm/possible_mass_market_manipulation_by_chinese/

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Umbrella litecoin hot crypto currency… Spikehttps://bittrex.com/Market/?MarketName=BTC-ULTChttps://bittrex.com/Market/?MarketName=BTC-ULTChttps://bittrex.com/Market/?MarketName=BTC-ULTChttps://bittrex.com/Market/?MarketName=BTC-ULTChttps://bittrex.com/Market/?MarketName=BTC-ULTC

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Blockchain of Ideas; Blockchain of Mathematical Ingenuity; Blockchain of Complex Analysis and Algebraic Geometry

The system of a circle’s folding into a cone and all of the mysteries within is the centerpiece of today’s most advanced mathematical understanding of reality and is the perfect language for beginning the esoteric learning and seeking of true esoteric knowledge.

A blockchain of ideas is what we find. Each new concept, vision or equation of understanding/description (phenomenologically) that develops leads to the potential of another new idea, but the solving or mental discovery of the new idea is the creation of the next block in the blockchain of mathematical development. The only difference between this and the way Bitcoin is arranged is that the Mathematical blockchain of discovery never ends. There is never a final block, and the rewards continue to grow.

All the Best,

Parker Emmerson

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Bitcoin Fat Finger August 1st 2014 (8-1-14) or Massive Buy? Dark Pool Settlement? Bitcoin Trades over $4300.00 (BTC $7000+ eye witness)

Is Bitcoin poised for a massive gain or was the event on August 1st 2014 just a fat finger accident. Did massive amounts of bitcoin exchange hands at massive prices around 22:00 hours UST? Did Bitcoin hit an all time high on August 1st 2014 of $7328.00 with an average price per BTC of $4417.90 on extra heavy trading? At around 5:00 in the afternoon, I got an alert on my phone from BTC Avg http://www.bitcoinaverage.com triggered by Bitcoin passing its all time nominal high of $1280.00 per each on Bitcoinaverage.com. I looked at my phone, and I couldn’t believe it, bitcoin had just traded at over $7300.00. I then went to Bitcoinaverage.com for actual confirmation of the volume. I couldn’t believe it. The average BTC price had jumped to $4300.00 across exchanges. There was double the volume in a single trade for the whole day. Somebody had exchanged over 17,000 bitcoins. Bitstamp was not reporting totals to the bitcoinaverage.com. A dark pool settlement occurs mostly outside of an exchange, or if provided by an exchange, is supposed to remain secret. It looks as though somebody may have leaked just one of these kinds of transactions intentionally or by accident.

If it was an accident, which exchange reported the data? Why is nobody investigating this? Why am I, a little blogger, the only one covering this at all so as to really get to the bottom of what happened?

I knew this wouldn’t last for long if it were an accident, and I knew someone would try to cover their tracks if it wasn’t an accident. I captured the screenshot from my phone while it still lasted. Moments later, this phenomenon vanished.

See:

Bitcoin Price Spike Hits All Time High from Revealed Dark Pool?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Could dark pools be trading BTC on dark wallets and dark exchanges, unnoticed by the greater trading community? Yes, they could be. Could they slip up and let us know the real price of bitcoin when you need to buy 17,000 of them? Yes, they could have.

Could this just be a glitch? Perhaps, let’s examine the evidence.

If you needed to buy 17,000 BTC, how would you get it? Who would be there to sell it to you? Prices seem to have settled back after the massive, seemingly unnoticed spike in the price, but perhaps most traders did not notice the slip up from the dark pool, where Bitcoin could be trading at massive all time highs due to the real volume. I have seen no other mention of what happened today with the price, so I felt obliged to post. Could a major player in the financials be getting into bit coin, resulting in a massive spike?

Local BTC was trading at over $900.00 at the time, and the other clue is that Bitstamp was not reporting figures at the time of the trade, but somehow, the feed kept going into Bitcoinaverage.com. Many, many Local BTC traders peg their pricing to the BitStamp.net spot. This leads me to think that Bitstamp settled a massive trade for a big player at a high BTC cost relative to the market, and the market was left undisturbed. People really didn’t notice, because it was masked relatively well on most exchanges. The order books would have gone out of control entirely and spiked the price of BTC permanently on a trade like that, creating massive volatility in the markets. Here, we see the principle of phenomenological velocity, the canceling of the volume while the trade actually takes place. If traders are looking for more BTC velocity, then look no further. Buy bit coin now.

Flat all day compared to the massive spike

Flat all day compared to the massive spike

With the bitcoin price’s exceeding $4300 per each bitcoin, some even settling for over $7000.00 each, the relative volatility for the rest of the day looked flat. You can probably still see this if you download the iphone app, btcReport on iPhone. We can see from the chart, that the bitcoin average price actually hit $1261.2 today. https://bitcoinaverage.com/markets#USD still reports that Bitstamp has been unreachable for a long time.

Furthermore, we can see that as noted, at 22:00-22:04, a flash spike in BTC took place. No data is published during that time, as it was just exactly between the cracks of reported trading on the official ledger at bitcoinaverage.com.

 

 

 

 

Here, we see how the official ledger does not mention the trade of BTC, some of which cost over $7300.00 (this is only my eye-witness account, because before I had a chance to think about capturing it on my phone, the price had slipped down under $4300.00).

How would the math work out here? What kind of formula could have been used to determine the cost of bitcoin for a “dark pool” settlement. With an average cost of bitcoin reported in the above example (exhibit), let’s assume $1261.00 for the average cost of bitcoin including the “fat finger” BTC or, “dark pool” exposed bitcoin sale.  The reported number of bitcoins sold was about 17800 BTC. 17800 * 1261 = $22,445,800, but the “real” reported average BTC cost is assumed to be $600.00, or about $10,680,000 daily volume. The difference is $11,765,800. So, we know the price of the dark pool bitcoins was between $1200-$7300.00 each. Let’s assume the average of those two prices as the cost per bitcoin. That would be $4250.00 per BTC. This number is somewhat evidenced, because after the $7300.00 figure, the price came down to ~$4400.00 and then even lower to around $1280.00. This tentatively indicates that only about 2768.42353 bitcoins were sold in a lump sum.

Conclusion: Hold your bit coins. Buy more bitcoins. We could see this price revealed to the entirety of the BTC market within the coming months and at that point, at what price will Dark Pools be trading bit coin?

 

Was this leaked by a dark pool or just a fat finger?

Dark Pool trade settlement or fat finger?

 

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Border Patrol = Cartels/Gangs

To whom it may concern:

It has come to my attention that people can freely come across the border from Mexico to America, but how can they make it?

The key here is that it’s cartel, gang, Mexican drug lords/hooligans that are the real border patrol. However, all it takes to get past them is about $500-$1000.00 cash.

Sometimes called Coyotes, these bands of marauders patrol the Mexican/American border and are the real border patrol. If you can’t pay these people, chances are you won’t get past them. They are incredibly numerous, and my contact in Mexico says that there is no way to get past them unless you pay.

You will also have to walk for six days (200 miles or more) through the dessert in order to make it to water and food. So, if you are a Mexican/immigrant and can pay $1000.00 and buy food and water, and carry it on your back for 6 days in the hot dessert, welcome to America, the door’s wide open.

All the Best,

iPhone

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By this post I claim original discovership on planet Earth (First) of this fact

©©©©©©©© PARKER EMMERSON ©©©©©©©©

Pi Approximation for the Aliens to Visit Me

This is the most accurate pi approximation in the known universe as discovered by Parker Emmerson, published 5-3-14

 

 

 

THIS IS A UNIQUE EXPRESSION, ONE THAT IS SO SO SO LARGE AND VAST THAT IT IS COPYRIGHTABLE BY ME. A STATEMENT, A PHRASE – COPYRIGHTED ON THIS DAY 5-3-14 by PARKER EMMERSON

1250442919173038756951025530092322508211776402059158997327709512/\
398028343281296922379798282700006993978049433204955287885364244 \
\[TildeTilde] \[Pi]

ANY ALIEN OR HUMAN WHO CAN SHOW ME THE DERIVATION OF THIS FACT CAN PROVE ME WRONG. OTHERWISE, THAT IS MY SECRET.

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JPM JP Morgan Going Belly Up

Sell JPM Short and buy gold, and buy silver. Sell sell sell!

http://www.silverdoctors.com/another-jpm-banker-dead-in-a-minivan-hit-run/

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Citizens Against Water Fluoridation Protest OWASA’s Illegal Acts

Water Fluoridation (Citizens Against It)

CITIZENS AGAINST WATER FLUORIDATION LETTER NUMBER ONE

Dear Town Council Members, OWASA, The Board of Aldermen and Citizens of Orange County, NC,

I hope all is well with you. I am writing to notify you that there is a toxic, hazardous substance currently added to the Orange County water supply. This substance is fluoride. After repeated inquiries into this matter with the OWASA board members, we have still not been told what kind of fluoride is added to the water. My peers who oppose the addition of the level 3 or 4 health hazard toxin known as fluoride suspect that the kind of fluoride currently added to the water is fluorosilic acid and that, when this kind of fluoride hits one’s stomach acid, it transforms into Hydrogen Fluoride, a level four (4) health hazard as rated by the NFPA fire diamonds seen:
http://en.wikipedia.org/wiki/Hydrogen_fluoride
http://en.wikipedia.org/wiki/NFPA_704 (Key to reading NFPA fire diamonds)
http://en.wikipedia.org/wiki/Sodium_fluoride (Level 3 Health Hazard, Toxic, Irritant)
http://en.wikipedia.org/wiki/Hexafluorosilicic_acid (Level 3 Health Hazard, Toxic, Corrosive)
http://www.sciencelab.com/msds.php?msdsId=9924083 (Level 3 Health Hazard)
http://toxnet.nlm.nih.gov/cgi-bin/sis/search/r?dbs+hsdb:@term+@rn+16961-83-4 (Level 4 Health Hazard)
Fluosilicic Acid: “Agent in water fluoridation, in preliminary treatment of hides and skins, and to reduce reflectivity in glass surfaces; disinfectant for copper and brass vessels; impregnating ingredient to preserve wood and to harden masonary; chem intermediate for aluminum trifluoride, cryolite, and fluorsilicates; electroplating agent for chromium.

Furthermore, Sodium fluoride pills are a prescription drug with NDC (National Drug Code) # 0288-1106-10 and NDC # 68032-382-12 (to name just two) – their primary purpose to deliver fluoride (fluorine) to the teeth through what I consider the pseudo-science of its being beneficial when contained in the saliva and “bathing the teeth” in fluoride continuously throughout the day. At least ten different citizens have challenged the OWASA board’s continued addition of fluoride (a by-product of the aluminum and fertilizer industries by their own admission on their website) with valid, cogent arguments against the addition of this drug into the water supply against their consent. We got nowhere with the board.

Notably – the recently dismissed “State Dentist” Rebecca King – gave her “testimony” (“expert” opinion) on the subject in a meeting that was exempt from public comment, and she used a tactic coined by Orwell as “Double Speak” on more than one occasion. She stated word for word, and I have this on record, “Fluoride is not a by-product of the fertilizer industry. Fluoride comes from the same phosphate rock that is used to create fertilizer – it does not come for fertilizer.” So, somehow these two things (phosphate mining and fertilizer production) are not correlated even though fluoride comes from the same phosphate rock used to produce fertilizer? If fluoride were not pumped into the public water supplies of practically every North Carolina township, what would the phosphate mining companies do with all of the fluoride? They would have to pay to dispose of it as what it is – toxic waste, which they do not want to do.

We confronted the OWASA board about this specific inconsistency in the pro-fluoride argument (position), among many, many others (for emphasis), and each time, they denied it – repeatedly stating that the fluoride they used did not come from the fertilizer and aluminum industries, until finally – Corey Sturmer, an anti-fluoride activist brought out into the open a print out of their own website (water quality report card) that stated their source of fluoride was phosphate rock from byproducts of the fertilizer and aluminum industry. Finally, they were forced to have one of their operational employees come to the meeting and give a statement about how the fluoride they used actually did come from the by-products of a North Carolina phosphate rock-mining plant which supplied the fertilizer industry. We have all of these encounters on video. This was just one example of misleading double-speak they used. They also denied direct response to our questions/points and neglected due diligence of researching the facts we presented to them. Otherwise, why would they have come to the decision to continue fluoridating the public water supply? We have them on record stating that it does not have a benefit to the safety of the water that so many people in this town drink.
They are not open about their actions, nor are they forthcoming with information that should be public. For example, I have asked them numerous times if they use sodium fluoride or a kind of fluorosilic acid, and they have not told me which one they use. I have asked them to address what gives them the right to give out a drug to unwitting people when they are admittedly not health professionals. They are the ones who add fluoride to the water and set the quantity of fluoride added. What are they doing adding fluoride to the water when they are not health professionals? They are not elected, but rather are an ad hoc committee. This goes against the constitution of North Carolina.

I am writing to implore you to re-examine the policies of the OWASA board. Think about these things, and ask yourself these questions:

The supposed purpose of the water fluoridation is supposedly for hardening the enamel of the teeth through the saliva. Fluoride has an NDC # (National Drug Code Number). Is it ethical to give a drug to everyone – or put otherwise – to discriminate against those who would not like to take the drug fluoride by forcing them to obtain fresh water sources and denying them public water?
If I drink one liter of OWASA water, I would be taking the equivalent of .7 mg of fluoride. If I were to drink to two liters of OWASA water, that means I would get 1.4 mgs of fluoride. The NDC # is relevant to doses of only .25 mg. per day. Think about that. This is huge over exposure if you are just drinking a regular amount of water. The board is drugging the population.
Could the right to freedom of religion be violated by the addition of a toxin to the water supply? Muslims must use clean water, free of toxins for their prayers. Fluoride is a toxin and health hazard. http://en.wikipedia.org/wiki/Hexafluorosilicic_acid FLUORIDES ARE LEVEL 3 and 4 HEALTH HAZARDS WITH CLASSIFCATIONS OF BOTH TOXIC AND CORROSIVE.
How can one ethically put a substance in the public water supply that has been linked to decreased bone density and lowered IQ in a Harvard Medical Journal study: http://www.hsph.harvard.edu/news/features/fluoride-childrens-health-grandjean-choi/
Has OWASA exceeded their charter in attempting to forcibly (covertly) drug the entire population? YES! OWASA’s charter allows them to provide clean water, not give drugs to the general population.
Fluoride pacifies people and makes them more complacent. This characteristic was used by Hitler, Stalin, and numerous other dictators to pacify the population and coerce them more easily into going along with totalitarian, facist ideologies. Why would we risk this in our own society by fluoridating the public?
WATER FLUORIDATION WAS JUST BANNED BY THE COUNTRY OF ISRAEL, STOPPED IN PORTLAND, OREGON AND IS GAINING MOMENTUM AS AN ISSUE OPPOSED BY AN AWAKENED PUBLIC.

The reality is that there a growing number of concerned citizens believe or at least question not only the validity of fluoride science, but the ethicality, potential of severely harmful side effects (on the human body through accumulation in the environment and over exposure), and true purpose of water fluoridation. We stand against water fluoridation whole-heartedly and believe fluoride should be avoided.

All Our Best,

PARKER EMMERSON AND THE UNDERSIGNED ATTACHED

X__________________________________

ADDITIONAL RESOURCES:
http://www.youtube.com/watch?v=aqQkqZKBuV4
http://www.youtube.com/watch?v=gyMlwv1pBKk
http://www.youtube.com/watch?v=GrovKbkEyIs
http://www.youtube.com/watch?v=6rTevKbkBzs
http://www.youtube.com/watch?v=hQ8qzDLZTZ8
http://www.youtube.com/watch?v=yRsWFghoPXM
http://www.youtube.com/watch?v=hYOllO4yM1o
http://www.youtube.com/watch?v=iFw5_9JdQ14
http://cameochemicals.noaa.gov/chemical/9070
http://en.wikipedia.org/wiki/Hexafluorosilicic_acid
http://en.wikipedia.org/wiki/Sodium_fluoride
http://www.youtube.com/watch?v=zFdwgpVCQQw
http://www.youtube.com/watch?v=R-0BhD6gebY
http://www.youtube.com/watch?v=ouNxYtCL32s
http://www.youtube.com/watch?v=gyMlwv1pBKk

 

OWASA IS IN VIOLATION OF GENERAL STATUTES:

http://www.ncga.state.nc.us/EnactedLegislation/Statutes/PDF/BySection/Chapter_90/GS_90-106.pdf

ReNaf Fluoride Tablets are Schedule

NC G.S. § 90-18.  Practicing without license; penalties.

OWASA is in DIRECT VIOLATION

§ 90-85.40.  Violations.

(a)        It shall be unlawful for any owner or manager of a pharmacy or other place to allow or cause anyone other than a pharmacist to dispense or compound any prescription drug unless that person is a pharmacy technician or a pharmacy student who is enrolled in a school of pharmacy approved by the Board and is working under the supervision of a pharmacist.

OWASA is in DIRECT VIOLATION

“The provision of drug therapy management by a licensed pharmacist engaged in the practice of pharmacy pursuant to an agreement that is physician, pharmacist, patient, and disease specific when performed in accordance with rules and rules developed by a joint subcommittee of the North Carolina Medical Board and the North Carolina Board of Pharmacy and approved by both Boards. Drug therapy management shall be defined as: (i) the implementation of predetermined drug therapy which includes diagnosis and product selection by the patient’s physician; (ii) modification of prescribed drug dosages, dosage forms, and dosage schedules; and (iii) ordering tests; (i), (ii), and (iii) shall be pursuant to an agreement that is physician, pharmacist, patient, and disease specific.”

http://www.ncga.state.nc.us/EnactedLegislation/Statutes/PDF/ByArticle/Chapter_90/Article_5.pdf

http://www.ncbop.org/LawsRules/Statutes.pdf

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