http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 23:54:42 GMT Wed, 10 Jun 2026 23:54:42 GMT The latest comments added to the Post, Stunningly beautiful identity proved http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144505 <p>Sergey Markelov is the author of the identity under consideration (2012). He states this is a root of</p> <p>8*x^9+(72*7^(1/3)-12)*x^6+(54*49^(1/3)-18*7^(1/3)+330)*x^3-(27*49^(1/3)+9*7^(1/3)+190) . Sergey Markelov refers to <a href="http://ru-math.livejournal.com/797774.html">http://ru-math.livejournal.com/797774.html</a> .</p> The latest comments added to the Post, Stunningly beautiful identity proved 144505 Tue, 12 Mar 2013 09:14:57 Z Markiyan Hirnyk Markiyan Hirnyk http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144525 <p><a href="http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved#comment144505">@Markiyan Hirnyk</a> At the bottom of Markelov's LiveJournal post to which you gave a link there a link to a 1988 article in Russian: <a href="http://kvant.mccme.ru/1988/06/tri_formuly_ramanudzhana.htm">http://kvant.mccme.ru/1988/06/tri_formuly_ramanudzhana.htm</a>. I don't read Russian, but it looks like this article attributes the formula to a Ramanujan. I am not sure. Could you check that please? </p> The latest comments added to the Post, Stunningly beautiful identity proved 144525 Tue, 12 Mar 2013 19:52:33 Z Carl Love Carl Love http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144528 <p>The cited article describes the proof of&nbsp; three trigonometrical&nbsp; formulas by Ramanujan. The formula of Markelov does not coincide with any of them. Also the one does not follow from them. Sergey Markelov uses the Ramanujan method and makes the reference on this.</p> <p>PS. In order to read a few sentences in Russian, you may use the Google translator.</p> <p>PPS. See <a href="/view.aspx?sf=144528/455930/screen12.03.13.docx">screen12.03.13.docx</a> .</p> The latest comments added to the Post, Stunningly beautiful identity proved 144528 Tue, 12 Mar 2013 20:30:04 Z Markiyan Hirnyk Markiyan Hirnyk http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144600 <p>Carl Love!&nbsp;</p> <p>Thanks for the elegant proof. I wonder <strong>whether can your approach&nbsp; find the value of LHS in the real radicals if RHS is unknown?</strong></p> <p>I propose a different proof of this remarkable identity in which &nbsp;directly constructed a polynomial, whose root is the value of LHS, and this is expressed in radicals. As this approach is completely unrelated to your method, I am creating a separate post.</p> The latest comments added to the Post, Stunningly beautiful identity proved 144600 Wed, 13 Mar 2013 23:12:43 Z Kitonum Kitonum http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144731 <pre>Here is my suggestion, somewhat late ... <br><br>Consider the LHS as expression of algebraic numbers (similar as Kitonum did) and use<br>the resolvent to find a polynomial, which has it as root by construction. <br><br>View at it as a polynomial in a cubic X = x^3 now try to solve for roots symbollically.<br><br>Amazingly Maple translates that to a polynomial over the integers - it simplifies the<br>trigonometric expression that way.<br><br>For the new polynomial it is easy to recognize RHS as root. And that both polynomials<br>are equal after norming them is 'proved' by the command 'is'.<br><br><br>It would be very nice to have that power of Maple not only hidden in 'RootOf' and 'is'.</pre> <pre><a href="/view.aspx?sf=144731/456312/trig_alg_resultan.mws">trig_alg_resultan.mws</a><br><a href="/view.aspx?sf=144731/456312/trig_alg_resultan.pdf">trig_alg_resultan.pdf</a><br><br>PS: I do not know, how to post that as 'answer' without a new thread ...</pre> The latest comments added to the Post, Stunningly beautiful identity proved 144731 Sun, 17 Mar 2013 22:20:13 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved?ref=Feed:MaplePrimes:Stunningly beautiful identity proved:Comments#comment144757 <p><a href="http://www.mapleprimes.com/posts/144499-Stunningly-Beautiful-Identity-Proved#comment144731">@Axel Vogt</a> Because of this reason I voted up your other good answer.</p> The latest comments added to the Post, Stunningly beautiful identity proved 144757 Mon, 18 Mar 2013 23:21:15 Z Markiyan Hirnyk Markiyan Hirnyk