Formula1 a:=(sqrt(exp(4*Pi)+exp(Pi)+1)*sqrt(exp(6*Pi)+exp(5*Pi)+exp(4*Pi)+exp(3*Pi)+2*exp(2*Pi)-2*exp(Pi)+1))/(sqrt(5)*sqrt(exp(2*Pi)+exp(Pi)+1)) ; \\ b:=(exp(6*Pi)+exp(5*Pi)+exp(4*Pi)+exp(3*Pi)-1)/(2*(exp(2*Pi)+exp(Pi)+1))-(sqrt(exp(4*Pi)+exp(Pi)+1)*sqrt(exp(6*Pi)+exp(5*Pi)+exp(4*Pi)+exp(3*Pi)+2*exp(2*Pi)-2*exp(Pi)+1))/(2*sqrt(5)*sqrt(exp(2*Pi)+exp(Pi)+1)) ; \\ phi:=a/(b+1/(1+exp(-Pi)/(1+exp(-2*Pi)/(1+exp(-3*Pi)/(1+exp(-4*Pi)/(1+exp(-Pi)/(1+exp(-2*Pi)/(1+exp(-3*Pi)/(1+exp(-4*Pi)/(1+…)))))))))) ; Le Mardi 10 octobre 2017 19h00, "math-fun-request@mailman.xmission.com" <math-fun-request@mailman.xmission.com> a écrit : Send math-fun mailing list submissions to math-fun@mailman.xmission.com To subscribe or unsubscribe via the World Wide Web, visit https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun or, via email, send a message with subject or body 'help' to math-fun-request@mailman.xmission.com You can reach the person managing the list at math-fun-owner@mailman.xmission.com When replying, please edit your Subject line so it is more specific than "Re: Contents of math-fun digest..." Today's Topics: 1. Golden Ratio (fran?ois mendzina essomba2) ---------------------------------------------------------------------- Message: 1 Date: Tue, 10 Oct 2017 03:40:08 +0000 (UTC) From: fran?ois mendzina essomba2 <m_essob@yahoo.fr> To: "math-fun@mailman.xmission.com" <math-fun@mailman.xmission.com> Subject: [math-fun] Golden Ratio Message-ID: <201334138.7974682.1507606808311@mail.yahoo.com> Content-Type: text/plain; charset=UTF-8 Hello,thank you foradding me in the Math-fun mailing list .I take thisopportunity to convey to you four formulas of the golden ratio.Thank you foryour timeand bestregards,formula 1:periodicity of order 4?a:=(sqrt(exp^(4*Pi)+exp^Pi+1)*sqrt(exp^(6*Pi)+exp^(5*Pi)+e^(4*Pi)+exp^(3*Pi)+2*exp^(2*Pi)-2*exp^Pi+1))/(sqrt(5)*sqrt(exp^(2*Pi)+e^Pi+1));?b:=(exp^(6*Pi)+exp^(5*Pi)+exp^(4*Pi)+exp^(3*Pi)-1)/(2*(exp^(2*Pi)+exp^Pi+1))-(sqrt(exp^(4*Pi)+exp^Pi+1)*sqrt(exp^(6*Pi)+exp^(5*Pi)+exp^(4*Pi)+exp^(3*Pi)+2*exp^(2*Pi)-2*exp^Pi+1))/(2*sqrt(5)*sqrt(exp^(2*Pi)+exp^Pi+1));?phi:=a/(b+1/(1+exp^(-Pi)/(1+exp^(-2*Pi)/(1+exp^(-3*Pi)/(1+exp^(-4*Pi)/(1+exp^(-Pi)/(1+exp^(-2*Pi)/(1+exp^(-3*Pi)/(1+exp^(-4*Pi)/(1+?))))))))));?formula 2: r:=(sqrt(exp^(4*Pi)+exp^Pi+1)*sqrt(exp^(6*Pi)+exp^(5*Pi)+exp^(4*Pi)+exp^(3*Pi)+2*exp^(2*Pi)-2*exp^Pi+1))/(sqrt(p)*sqrt(exp^(2*Pi)+exp^Pi+1));a:=? ((p-1)/4)*r;b:=(exp^(6*Pi)+exp^(5*Pi)+exp^(4*Pi)+exp^(3*Pi)-1)/(2*(exp^(2*Pi)+exp^Pi+1))-(sqrt(exp^(4*Pi)+exp^Pi+1)*sqrt(exp^(6*Pi)+exp^(5*Pi)+exp^(4*Pi)+exp^(3*Pi)+2*exp^(2*Pi)-2*exp^Pi+1))/(2*sqrt(p)*sqrt(exp^(2*Pi)+exp^Pi+1));j:=a/(b+1/(1+exp^(-Pi)/(1+exp^(-2*Pi)/(1+exp^(-3*Pi)/(1+exp^(-4*Pi)/(1+exp^(-Pi)/(1+exp^(-2*Pi)/(1+exp^(-3*Pi)/(1+exp^(-4*Pi)/(1+?))))))))));j?:=(sqrt(p)+1)/2?;?formula3;periodicity of order 4 ;a:=sqrt(7132129815550981725745577127418524500105436241812778561)/(4983267051713428905499820187*sqrt(5));b:=-(sqrt(7132129815550981725745577127418524500105436241812778561)+2670593656810572179193662447*sqrt(5))/(9966534103426857810999640374*sqrt(5));phi:=a/(b+1/(1+1^1/(1+2^2/(1+3^3/(1+4^4/(1+5^5/(1+6^6/(1+7^7/(1+8^8/(1+9^9/(1+10^10/(1+11^11/(1+1^1/(1+2^2/(1+3^3/(1+4^4/(1+5^5/(1+6^6/(1+7^7/(1+8^8/(1+9^9/(1+10^10/(1+11^11/(1+? ))))))))))))))))))))))));?formula4?;?165580141*phi^(-1)-102334155=1/(sqrt(1+370248451*sqrt(1+370248451*sqrt(1+370248451*sqrt(1+370248451*sqrt(1+...))))));? ------------------------------ Subject: Digest Footer _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun ------------------------------ End of math-fun Digest, Vol 176, Issue 12 *****************************************