Discussion:
New trigonometric proof for Fermat's Last Theorem
(too old to reply)
Arindam Banerjee
2022-04-05 08:40:05 UTC
Permalink
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
Arindam Banerjee
2022-04-08 23:25:37 UTC
Permalink
Post by Arindam Banerjee
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
Arindam Banerjee
2022-04-18 02:00:08 UTC
Permalink
Post by Arindam Banerjee
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
Arindam Banerjee
2022-04-26 07:13:49 UTC
Permalink
Post by Arindam Banerjee
Post by Arindam Banerjee
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

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