EVALUATIONS/SOLUTIONS by Wolframalfa
EVALUATIONS/SOLUTIONS BY WolframAlfa.
FORMULAE/ EQUATIONS DESIGNED BY PANAGIOTIS STEFANIDES
©Copyright by Panagiotis Chr. Stefanides
P.Stefanides
http://www.wolframalpha.com/input/?i=T%5E4+-T%5E2+-1+%3D0&asynchronous=false&equal=Submit
T^4 -T^2 -1 =0
FOMULA DERIVED FROM PLATO'S TIMAEUS “MOST BEAUTIFUL TRIANGLE"
AS PROPOSED TO VARIOUS NATIONAL AND INTERNATIONAL CONFERENCES BY PANAGIOTIS STEFANIDES:
http://www.stefanides.gr/pdf/BOOK%20_GRSOGF.pdf
COPYRIGHT BY PANAGIUOTIS STEFANIDES
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http://www.wolframalpha.com/input/?i=ln%5Bln%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D+-+ln%5B+ln%5Bsqrt%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D%5D%3D+
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http://www.wolframalpha.com/input/?i=4%2F+SQRT[[sqrt%285%29%2B1]+%2F+2]
http://www.wolframalpha.com/input/?i=ln+%5B+%5Bsqrt%5B5%5D%2B1%5D%2FX+%5D%3Dln%5Bln%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D+-+ln%5B+ln%5Bsqrt%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D%5D+&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=%5Btan%2845%29+%5Bsqrt%285%29+tan%2845%29%5D+%2F+%5B+e%5E%5Bln%7B2%2A%5B%28sqrt%285%29+tan%2845%29%29%2F2+%5D%5E4%7D%2F%7B%5B%5Bsqrt%285%29+tan%2845%29%5D%2F2%5D%5E2%7D%5D%5D%5E%7B%5Bln%5Bln%5BX%5D%5D+%5...D+-+ln%5Bln%5Bsqrt%5BX%5D%5D%5D%7D%5D%5E0.25%3Dsqrt%5B%CE%A6%5D%3D%CE%A4&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=4%2F+SQRT%5B%5Bsqrt%285%29%2B1%5D+%2F+2%5D
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http://www.wolframalpha.com/input/?i=%5Bsqrt%285%29%2B1%5D+%2F+e%5E%7B%5Bln%5Bln%5BX%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5BX%5D%5D%5D%7D+%3D+&asynchronous=false&equal=SubmitEVALUATION BY WolframAlfa.
FORMULA DESIGN BY PANAGIOTIS STEFANIDES
COPYRIGHT PANAGIOTIS STEFANIDES
http://www.wolframalpha.com/input/?i=[ln[ln[1.1]]+%2A90]+-+ln[ln[sqrt[1.1]]]%2A90
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http://www.wolframalpha.com/input/?i=%5Bln%5Bln%5B1.1%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5B1.1%5D%5D%5D%3D+ln%5B%5Bsqrt%285%29%2B1%5D%2FPhi%5D&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=%5B1%2Fx%5D%5E12-%5B1%2Fx%5D%5E11%2B%5B1%2Fx%5D%5E10-%5B1%2Fx%5D%5E9-%5B1%2Fx%5D%5E8-%5B1%2Fx%5D%5E5-%5B1%2Fx%5D%5E4%2B%5B1%2Fx%5D%5E3-%5B1%2Fx%5D%5E2%2B1%3D0#fb
http://www.wolframalpha.com/input/?i=ln%5Bln%5BZ%5D%5D++-+ln%5Bln%5Bsqrt%5BY%5D%5D%5D+%3D+ln+2&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=%5Btan%2845%29%2B%5Bsqrt%285%29%2B1%5D+%2F+e%5E%7B%5Bln%5Bln%5B1.1%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5B1.1%5D%5D%5D%7D%5D%5E0.25+%3D+&asynchronous=false&equal=SubmitEVALUATION
http://www.wolframalpha.com/input/?i=%5Bsqrt%285%29%2B1%5D+%2F+e%5E%7B%5Bln%5Bln%5B11%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5B11%5D%5D%5D%7D+%3D+&asynchronous=false&equal=SubmitFORMULA
http://www.wolframalpha.com/input/?i=[1.34217728+%C3%97+10%5E8]%2A2.2360679774997896964091736687312762354406183596115257+&dataset&asynchronous=false&equal=Submit FORMULA STEFANIDES PROPOSITION FOR SPEED OF LIGHT.
http://www.wolframalpha.com/input/?i=+%5B+%5Bsqrt%5B5%5D%2B1%5D%2FX+%5D%3D%5Bln%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D%2F%5B+ln%5Bsqrt%5B%5Bsqrt%285%29+%2B+1%5D%2F2%5D%5D%5D+&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=+X%5E6-3X%5E4%2BX%5E2%2B2%3D0&asynchronous=false&equal=Submit
http://www.wolframalpha.com/input/?i=x%5E6-x%5E4+-x%5E2%3D+0&asynchronous=false&equal=Submit
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http://www.wolframalpha.com/input/?i=tan%2845%29%2B%5Bsqrt%285%29%2Btan%2845%29%5D+%2F+%5B+e%5E%5Bln%7B2*%5B%28sqrt%285%29%2Btan%2845%29%29%2F2+%5D%5E4%7D%2F%7B%5B%5Bsqrt%285%29%2B1%5D%2F2%5D%5E2%7D%5D%5D%5E%7B%5Bln%5Bln%5B0%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5B0%5D%5D%5D%7D+%3D+&asynchronous=false&equal=Submit
http://www.wolframalpha.com/input/?i=tan%2845%29%2B%5Bsqrt%285%29%2B1%5D+%2F+e%5E%7B%5Bln%5Bln%5B1.1%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5B1.1%5D%5D%5D%7D+%3D+&asynchronous=false&equal=Submit
http://www.wolframalpha.com/input/?i=tan%2845%29%2B%5Bsqrt%285%29%2B1%5D+%2F+%5B+e%5E%5Bln%7B2*%5B%28sqrt%285%29%2Btan%2845%29%29%2F2+%5D%5E4%7D%2F%7B%5B%5Bsqrt%285%29%2Btan%2845%29%5D%2F2%5D%5E2%7D%5D%5D%5E%7B%5Bln%5Bln%5BX%5D%5D+%5D+-+ln%5Bln%5Bsqrt%5BX%5D%5D%5D%7D+%3D+&asynchronous=false&equal=Submit
http://www.wolframalpha.com/input/?i=X%5E12-X%5E11%2BX%5E10-X%5E9-X%5E8-X%5E5-X%5E4%2BX%5E3-X%5E2%2B1%3D0&asynchronous=false&equal=Submit
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Wolfram|Alpha Feedback Team
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3/7/2011 1:38 pm
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Input: [tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ 62.38324625/90]/0.999984909 ] - ln[31.19162313/90]/0.999984909]}]^0.25= tan[51.82729129]
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA:
P[tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ 62.38324625/90]/0.999984909 ] - ln[31.19162313/90]/0.999984909]}]^0.25= tan[51.82729129]
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Input: [tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ 62.38324625/90] ] - ln[31.19162313/90]]}]^0.25= tan[51.82729129]
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA:
[tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ 62.38324625/90] ] - ln[31.19162313/90]]}]^0.25= tan[51.82729129
© Copyright Panagiotis Ch. Stefanides 2 JULY 2011
Thank you for your message regarding Wolfram|Alpha. We are continually working to improve Wolfram|Alpha, so all feedback is very much appreciated.
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Input: [tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ 62.38324625/90] ] - ln[31.19162313/90]]}]^0.25=
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA FOR;
X = 2 , Θ1 = 62.38324625,
ln[2]=62.38324625/90 = 0.693147181
SQRT[X] = SQRT[2] = 1.414213562 , Θ2=31.19162313
ln[SQRT[2]]= 31.19162313/90 = 0.34657359
© Copyright Panagiotis Ch. Stefanides 2 JULY 2011
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Input: [tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ln[X]] ] - ln[ln[sqrt[X]]]}]^0.25=sqrt[Φ]=Τ
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA:
[tan(45)+[sqrt(5)+tan(45)] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ln[X]] ] - ln[ln[sqrt[X]]]}]^0.25=sqrt[Φ]=Τ
© Copyright Panagiotis Ch. Stefanides 02/07/2011
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Input: e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]=
Occupation: Chartered Engineer [UK]
Organization:
Message:
PANAGIOTIS STEFANIDES FORMULA:
e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]=
[CALCULATED TO BE 2.718240808 BY HAND HELD SCIENTIFIC TEXAS INSTRUMENTS TI-30XA ]
© Copyright Panagiotis Ch. Stefanides 2 July 2011
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Input: tan(45)+[sqrt(5)+1] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ln[X]] ] - ln[ln[sqrt[X]]]} =
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA:
tan(45)+[sqrt(5)+1] / [ e^[ln{2*[(sqrt(5)+tan(45))/2 ]^4}/{[[sqrt(5)+tan(45)]/2]^2}]]^{[ln[ln[X]] ] - ln[ln[sqrt[X]]]} =
© Copyright Panagiotis Ch. Stefanides 2 July 2011
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Input: ln [ [sqrt[5]+1]/GOLDEN RATIO] ]=ln[ln[[sqrt(5) + 1]/2]] - ln[ ln[sqrt[[sqrt(5) + 1]/2]]]
Occupation: Chartered Engineer [UK]
Organization:
Message: ln [ [sqrt[5]+1]/GOLDEN RATIO] ]=ln[ln[[sqrt(5) + 1]/2]] - ln[ ln[sqrt[[sqrt(5) + 1]/2]]]
© Copyright Panagiotis Ch. Stefanides 7 JULY 2011
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Input: tan(45)+[sqrt(5)+1] / e^{[ln[ln[1.1]] ] - ln[ln[sqrt[1.1]]]} =
Occupation: Chartered Engineer [UK]
Organization:
Message: PANAGIOTIS STEFANIDES FORMULA:
tan(45)+[sqrt(5)+1] / e^{[ln[ln[1.1]] ] - ln[ln[sqrt[1.1]]]} =
© Copyright Panagiotis Ch. Stefanides 02/07/2011
1.618... 1.618.. PANAGIOTIS STEFANIDES FORMULA
Τέλος φόρμας
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» | Documentation | Properties | Definition
» | Documentation | Properties | Definition
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Αρχή φόρμας
/Your input: Y=Tan{ArcCos[SQRT(1/ [ (1/{[1/[Sin{ArcTan[1.6180339887498948482045868343656381]}]^2]-1})+1])]}
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Input:
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Exact result:
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Decimal approximation:
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Continued fraction:
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