• New trigonometric proof for Fermat's Last Theorem

    From Arindam Banerjee@21:1/5 to All on Tue Apr 5 01:40:05 2022
    In 17th century style I wrote it on paper.
    I posted it just now in my facebook timeline. Now that is publication so far as I am concerned.
    https://www.facebook.com/arindam.banerjee.31149359/
    Basically the idea is that the interior angles should sum up to pi/2 if there is a solution for n=3 for the famous relation.
    I did an Excel sheet, and the nearest I got was 1.569155609
    That was using Taylor expansion using 5 terms.
    Going by the spread I doubt if we could make it to 1.570796

    Don't know if the world will accept this as a proof, just that it may be a new approach which could lead to ways to find multiple solutions (non-integer) for a^n+b^n=c^n by targeting on the most like a/c ratio.

    Cheers,
    Arindam Banerjee

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  • From Arindam Banerjee@21:1/5 to Arindam Banerjee on Fri Apr 8 16:25:37 2022
    On Tuesday, 5 April 2022 at 18:40:06 UTC+10, Arindam Banerjee wrote:
    In 17th century style I wrote it on paper.
    I posted it just now in my facebook timeline. Now that is publication so far as I am concerned.
    https://www.facebook.com/arindam.banerjee.31149359/
    Basically the idea is that the interior angles should sum up to pi/2 if there is a solution for n=3 for the famous relation.
    I did an Excel sheet, and the nearest I got was 1.569155609
    That was using Taylor expansion using 5 terms.
    Going by the spread I doubt if we could make it to 1.570796

    Don't know if the world will accept this as a proof, just that it may be a new approach which could lead to ways to find multiple solutions (non-integer) for a^n+b^n=c^n by targeting on the most like a/c ratio.

    Cheers,
    Arindam Banerjee
    My proof of FLT has been approved by my Indian colleagues, who are highly trained and discerning scientists and engineers.
    I have no doubt that in due course it will be universally accepted.
    After all, I have made it all so simple, that clever high school students can easily understand.

    https://www.facebook.com/photo?fbid=5686846731343077&set=pcb.5686846781343072

    I would very much like this bit of paper to be sold!

    Would help my work in Internal Force Engines.
    Cheers,
    Arindam Banerjee

    x theta phi sum
    0.001 3.16228E-05 1.316691467 1.31672309
    0.011 0.00115369 1.316689831 1.31784352
    0.021 0.003043194 1.316680073 1.319723267
    0.031 0.00545814 1.316654812 1.322112952
    0.041 0.008301963 1.316606666 1.324908628
    0.051 0.011517676 1.316528254 1.328045931
    0.061 0.015066459 1.316412202 1.33147866
    0.071 0.018919665 1.316251136 1.3351708
    0.081 0.023055047 1.316037691 1.339092738
    0.091 0.027454697 1.315764514 1.34321921
    0.101 0.032103817 1.315424259 1.347528075
    0.111 0.03698993 1.315009599 1.351999529
    0.121 0.042102353 1.314513225 1.356615578
    0.131 0.047431821 1.313927849 1.361359671
    0.141 0.052970221 1.313246213 1.366216434
    0.151 0.058710387 1.312461087 1.371171474
    0.161 0.064645954 1.311565279 1.376211233
    0.171 0.070771232 1.310551637 1.381322869
    0.181 0.077081118 1.309413057 1.386494175
    0.191 0.083571019 1.308142487 1.391713505
    0.201 0.090236789 1.306732932 1.396969721
    0.211 0.097074686 1.305177465 1.40225215
    0.221 0.104081324 1.303469225 1.407550548
    0.231 0.111253644 1.301601432 1.412855075
    0.241 0.118588883 1.299567389 1.418156272
    0.251 0.126084552 1.297360491 1.423445043
    0.261 0.133738412 1.29497423 1.428712643
    0.271 0.141548463 1.292402205 1.433950668
    0.281 0.149512923 1.289638124 1.439151047
    0.291 0.15763022 1.286675817 1.444306037
    0.301 0.16589898 1.28350924 1.44940822
    0.311 0.17431802 1.28013248 1.4544505
    0.321 0.182886335 1.276539767 1.459426102
    0.331 0.191603101 1.272725473 1.464328575
    0.341 0.200467663 1.268684127 1.469151789
    0.351 0.209479531 1.264410411 1.473889943
    0.361 0.218638384 1.259899176 1.47853756
    0.371 0.227944059 1.255145438 1.483089497
    0.381 0.237396556 1.250144386 1.487540942
    0.391 0.246996034 1.244891387 1.491887421
    0.401 0.256742815 1.239381987 1.496124801
    0.411 0.266637379 1.233611913 1.500249292
    0.421 0.276680371 1.227577078 1.504257449
    0.431 0.286872603 1.221273574 1.508146177
    0.441 0.297215053 1.214697681 1.511912734
    0.451 0.307708874 1.207845855 1.515554728
    0.461 0.318355393 1.200714733 1.519070125
    0.471 0.329156122 1.193301123 1.522457245
    0.481 0.34011276 1.185602002 1.525714762
    0.491 0.351227204 1.177614503 1.528841707
    0.501 0.362501551 1.169335911 1.531837462
    0.511 0.373938114 1.160763646 1.53470176
    0.521 0.385539427 1.151895255 1.537434682
    0.531 0.397308258 1.142728389 1.540036647
    0.541 0.40924762 1.133260793 1.542508412
    0.551 0.421360786 1.123490276 1.544851062
    0.561 0.433651306 1.113414693 1.547065999
    0.571 0.446123017 1.103031917 1.549154935
    0.581 0.458780069 1.092339807 1.551119876
    0.591 0.471626939 1.081336174 1.552963113
    0.601 0.484668457 1.070018743 1.5546872
    0.611 0.497909827 1.058385113 1.55629494
    0.621 0.511356656 1.046432704 1.55778936
    0.631 0.525014981 1.034158712 1.559173693
    0.641 0.538891303 1.021560042 1.560451345
    0.651 0.55299262 1.008633249 1.561625869
    0.661 0.567326464 0.995374466 1.56270093
    0.671 0.581900946 0.981779317 1.563680263
    0.681 0.596724799 0.967842832 1.564567631
    0.691 0.61180743 0.953559346 1.565366776
    0.701 0.627158971 0.938922382 1.566081353
    0.711 0.642790342 0.923924526 1.566714868
    0.721 0.658713316 0.90855728 1.567270596
    0.731 0.674940587 0.892810896 1.567751484
    0.741 0.691485852 0.87667419 1.568160042
    0.751 0.708363893 0.860134316 1.568498209
    0.761 0.725590669 0.84317652 1.568767189
    0.771 0.743183421 0.825783838 1.568967259
    0.781 0.761160779 0.807936742 1.569097521
    0.791 0.779542882 0.789612728 1.569155609
    0.801 0.798351511 0.770785804 1.569137315
    0.811 0.817610232 0.751425884 1.569036116
    0.821 0.837344549 0.731498026 1.568842575
    0.831 0.857582075 0.710961494 1.568543569
    0.841 0.878352717 0.689768568 1.568121285
    0.851 0.899688875 0.667863019 1.567551895
    0.861 0.921625662 0.645178119 1.566803781
    0.871 0.944201138 0.621634002 1.56583514
    0.881 0.967456569 0.597134091 1.56459066
    0.891 0.991436708 0.571560133 1.562996841
    0.901 1.016190096 0.544765148 1.560955244
    0.911 1.041769392 0.516563053 1.558332446
    0.921 1.068231732 0.486712867 1.554944599
    0.931 1.095639111 0.454893512 1.550532623
    0.941 1.124058808 0.420661378 1.544720186
    0.951 1.153563835 0.383373496 1.536937331
    0.961 1.184233431 0.342034643 1.526268074
    0.971 1.216153593 0.294949151 1.511102744
    0.981 1.24941765 0.238743812 1.488161462
    0.991 1.284126884 0.164316321 1.448443204

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  • From Arindam Banerjee@21:1/5 to Arindam Banerjee on Sun Apr 17 19:00:08 2022
    On Tuesday, 5 April 2022 at 18:40:06 UTC+10, Arindam Banerjee wrote:
    In 17th century style I wrote it on paper.
    I posted it just now in my facebook timeline. Now that is publication so far as I am concerned.
    https://www.facebook.com/arindam.banerjee.31149359/
    Basically the idea is that the interior angles should sum up to pi/2 if there is a solution for n=3 for the famous relation.
    I did an Excel sheet, and the nearest I got was 1.569155609
    That was using Taylor expansion using 5 terms.
    Going by the spread I doubt if we could make it to 1.570796

    Don't know if the world will accept this as a proof, just that it may be a new approach which could lead to ways to find multiple solutions (non-integer) for a^n+b^n=c^n by targeting on the most like a/c ratio.

    Cheers,
    Arindam Banerjee

    https://www.facebook.com/photo.php?fbid=5686846731343077&set=a.3856470274380741&type=3&comment_id=5715352665159150&reply_comment_id=5717829131578170&force_theater=true&notif_id=1650063854713120&notif_t=photo_comment&ref=notif

    provided comments, about clarifying the method and future work

    --- SoupGate-Win32 v1.05
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  • From Arindam Banerjee@21:1/5 to Arindam Banerjee on Tue Apr 26 00:13:49 2022
    On Monday, 18 April 2022 at 12:00:09 UTC+10, Arindam Banerjee wrote:
    On Tuesday, 5 April 2022 at 18:40:06 UTC+10, Arindam Banerjee wrote:
    In 17th century style I wrote it on paper.
    I posted it just now in my facebook timeline. Now that is publication so far as I am concerned.
    https://www.facebook.com/arindam.banerjee.31149359/
    Basically the idea is that the interior angles should sum up to pi/2 if there is a solution for n=3 for the famous relation.
    I did an Excel sheet, and the nearest I got was 1.569155609
    That was using Taylor expansion using 5 terms.
    Going by the spread I doubt if we could make it to 1.570796

    Don't know if the world will accept this as a proof, just that it may be a new approach which could lead to ways to find multiple solutions (non-integer) for a^n+b^n=c^n by targeting on the most like a/c ratio.

    Cheers,
    Arindam Banerjee
    https://www.facebook.com/photo.php?fbid=5686846731343077&set=a.3856470274380741&type=3&comment_id=5715352665159150&reply_comment_id=5717829131578170&force_theater=true&notif_id=1650063854713120&notif_t=photo_comment&ref=notif

    provided comments, about clarifying the method and future work

    Well, looks like I actually disproved - with the help of Don Travis - the FLT when I thought I had proved it.
    My mistake had been to take only the first five terms of an infinite series.
    So even the asin function in Excel gives

    arcsin(sqrt(x^n) + arcsin(sqrt(1-x^n) = pi/2
    which turns out to be a brand new inverse trigonometric indentity
    whose use is presently unknown!

    Cheers,
    Arindam Banerjee

    --- SoupGate-Win32 v1.05
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