tag:blogger.com,1999:blog-12535639.post114081378457772433..comments2021-04-02T00:42:48.223-07:00Comments on Fermat's Last Theorem: Euler's FormulaLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-12535639.post-22345718171149010802010-12-17T23:50:05.978-08:002010-12-17T23:50:05.978-08:00Though this proves the desired result, it doesn...Though this proves the desired result, it doesn't come out of intuition like the previous simpler proof..Sanjuhttps://www.blogger.com/profile/13991247227351294410noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-36545781414391682862009-03-23T22:23:00.000-07:002009-03-23T22:23:00.000-07:00This theorem resulted in a breakthrough in mathema...This theorem resulted in a breakthrough in mathematics. Before, imaginary exponents were undefined. This theorem introduced imaginary exponents, as well as logarithms of numbers that are not positive and real.Michael Ejercitohttps://www.blogger.com/profile/10707862691472293497noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-55852581977088546092007-02-13T14:20:00.000-08:002007-02-13T14:20:00.000-08:00When compared to other silly blogs, yours seems to...When compared to other silly blogs, yours seems to me like "God among insects". Keep the good work bro.batujhttps://www.blogger.com/profile/05239502435488411142noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1165259572181798202006-12-04T11:12:00.000-08:002006-12-04T11:12:00.000-08:0012 04 06What a great blog you have here!!! I did a...12 04 06<BR/><BR/>What a great blog you have here!!! I did a similar derivation of the Inverse tangent function using these same principles. But the explicit representation for Tan^-1 came out algebraically. <A HREF="http://mrigmaiden.blogspot.com/2006/11/josh-euler-relations-inverse-tangent_14.html" REL="nofollow">See here</A>. Meanwhile I will blogroll you:)Legacy Userhttps://www.blogger.com/profile/06003763279963160818noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1163030777277156152006-11-08T16:06:00.000-08:002006-11-08T16:06:00.000-08:00This formula can be interpreted as saying that the...This formula can be interpreted as saying that the function eix traces out the unit circle in the complex number plane as x ranges through the real numbers. Here, x is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counter clockwise and in radians The formula is valid only if sin and cos take their arguments in radians rather than in degrees.<BR/>source: Wikipedia<BR/><BR/>For x=pi, the equation is <BR/>e^ipi = -1 or e^ipi + 1 = 0 or<BR/>e^ipi = 0 - 1 ; ln [e^ipi] = ln [0/1]; hence, ipi = ln [0] = 0 ;<BR/>e^0 = 1 ; 1 + 1 = 0 (mod 2)= 2<BR/><BR/>See 'Proof' by David Auburn(p.73-4)<BR/>"Let X equal the quantity of all quantities of X. Let X equal the cold ... months [11, 12, 1, 2] ... and four of heat [5, 6, 7, 8] leaving four months of in-/determine temperature [2,3,9,10].<BR/>[The months are a unit circle, and the Euler equation is its design. The indetermined area is undefined as is the definition of infinite.]<BR/>"Let X equal the month of full bookstores [infinite or undefined as month 10]. The number of books approaches infinity as the number of months of cold approaches four."<BR/><BR/>The 'proof' is also a statement of:<BR/><BR/>cos x = e^ix + e^[-ix] (over 2)and<BR/>sin x = e^ix - e^[-ix] (over 2i)<BR/><BR/>solving for both cos x and sin x<BR/>cos pi = e^ipi + 1/1 = 2 = <BR/>0 (mod 2) = -1<BR/>sin pi = 1 - 1 = 0<BR/><BR/>e^ipi = cos pi + isin pi = -1 + 0<BR/>sin pi - cos pi = 2 = 0 (mod 2)<BR/><BR/>The 'proof' is a restatement of Fermat's Last Theorem for modular formulation of infinite number of primes, in the transformation of finite to infinite, using a modular clock function: <BR/>a unit circle in the complex number plane. "Let X equal the number ...."professionahttps://www.blogger.com/profile/02159466883720249144noreply@blogger.com