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Groups > sci.math > #436507 > unrolled thread
| Started by | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| First post | 2019-03-06 21:45 -0800 |
| Last post | 2019-03-17 12:31 -0700 |
| Articles | 15 on this page of 35 — 8 participants |
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AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-06 21:45 -0800
Re: AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity eastside.erik@gmail.com - 2019-03-07 08:16 -0800
Re: AP's 2014 incorrect proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-03-07 18:41 +0000
Re: AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-07 14:21 -0800
My 1993 basis vector pure algebra proof of Regular FLT Re: AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-08 21:32 -0800
AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-09 12:39 -0800
AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-09 18:59 -0800
Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity eastside.erik@gmail.com - 2019-03-09 20:16 -0800
a pure algebra proof of Generalized FLT Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-09 22:41 -0800
a pure algebra proof of Generalized FLT Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Mike Hart <gmoralesor@gmail.com> - 2019-03-10 03:35 -0700
Re: a pure algebra proof of Generalized FLT Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Peter Percival <peterxpercival@hotmail.com> - 2019-03-10 13:11 +0000
Yes, integers form a vector space as do all Grid Number systems //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 13:01 -0700
Re: Yes, integers form a vector space as do all Grid Number systems //updated 2019 for more clarity Peter Percival <peterxpercival@hotmail.com> - 2019-03-11 16:59 +0000
in Generalized we need only FACTOR, not prime factor Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 12:45 -0700
Re: in Generalized we need only FACTOR, not prime factor Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Alan Mackenzie <acm@muc.de> - 2019-03-10 22:30 +0000
Re: in Generalized we need only FACTOR, not prime factor Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity eastside.erik@gmail.com - 2019-03-10 15:39 -0700
Eastside suggests ignorant fools of math who cannot understand AP's proof ellipse is never a conic (see below) Stefan Mueller, Christopher Ohrt, Donald Ornstein, George Papanicolaou, Lenya Ryzhik, Stanford Univ Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 16:45 -0700
Re: a pure algebra proof of Generalized FLT Re: AP's original proof of FLT back in 1993 is a true pure algebra proof of FLT --basis vector or additive-multiplicative-identity //updated 2019 for more clarity Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 15:04 -0700
proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 22:23 -0700
proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Mike Hart <gmoralesor@gmail.com> - 2019-03-10 23:00 -0700
proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-10 23:32 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Alan Mackenzie <acm@muc.de> - 2019-03-11 09:53 +0000
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 eastside.erik@gmail.com - 2019-03-11 10:02 -0700
Jennifer Wilson, Alex Wright, Lexing Ying, Xuwen Zhu, of Stanford Univ, are you as stupid as Eastside to never understand Real Proton = 840 MeV with electron= muon and .5MeV was Dirac magnetic monopole// ellipse is never a conic (see proof below) Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-11 19:32 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-11 20:24 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Mike Hart <gmoralesor@gmail.com> - 2019-03-12 05:44 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-12 12:01 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Mike Hart <gmoralesor@gmail.com> - 2019-03-12 12:11 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 eastside.erik@gmail.com - 2019-03-12 12:14 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2019-03-12 12:30 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 Mike Hart <gmoralesor@gmail.com> - 2019-03-12 13:50 -0700
Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 eastside.erik@gmail.com - 2019-03-12 15:40 -0700
Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test moroney@world.std.spaamtrap.com (Michael Moroney) - 2019-03-10 17:08 +0000
Re: AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity j4n bur53 <janburse@fastmail.fm> - 2019-03-10 21:00 +0100
Re: AP's 2014 proof of Generalized FLT Fermat's Last Theorem and proof of Regular FLT as a corollary thereof//updated 2019 for more clarity j4n bur53 <bursejan@gmail.com> - 2019-03-17 12:31 -0700
Page 2 of 2 — ← Prev page 1 [2]
| From | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| Date | 2019-03-10 23:32 -0700 |
| Subject | proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <d5f3efbd-476e-4982-981a-fcdea81e7c45@googlegroups.com> |
| In reply to | #436804 |
Why not read my first post in this thread? > >What is Generalized FLT? Glad you asked, for it is: A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2 FLT is of course A^n + B^n = C^n where A,B,C, n are positive integers and n is greater than 2
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2019-03-11 09:53 +0000 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <q65b6p$2a9u$1@news.muc.de> |
| In reply to | #436807 |
Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote: > Why not read my first post in this thread? Because it's 483 lines long, and rambling. >> >>What is Generalized FLT? Glad you asked, for it is: > A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z > greater than 2 That is not the statement of a theorem. It is merely an equation relating 6 integers. What about those 6 integers? What does the generalised FLT say about them? > FLT is of course > A^n + B^n = C^n where A,B,C, n are positive integers and n is greater > than 2 No. The essence of the FLT is that no such integers exist, and this needs to be explicitly stated. The FLT has been proved. -- Alan Mackenzie (Nuremberg, Germany).
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| From | eastside.erik@gmail.com |
|---|---|
| Date | 2019-03-11 10:02 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <a21cac4a-0dc9-41ed-8c03-329a75306e71@googlegroups.com> |
| In reply to | #436828 |
On Monday, March 11, 2019 at 2:53:36 AM UTC-7, Alan Mackenzie wrote: > Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote: > > Why not read my first post in this thread? > > Because it's 483 lines long, and rambling. > > >> > >>What is Generalized FLT? Glad you asked, for it is: > > > A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z > > greater than 2 > > That is not the statement of a theorem. It is merely an equation > relating 6 integers. What about those 6 integers? What does the > generalised FLT say about them? > > > FLT is of course > > > A^n + B^n = C^n where A,B,C, n are positive integers and n is greater > > than 2 > > No. The essence of the FLT is that no such integers exist, and this > needs to be explicitly stated. The FLT has been proved. > > -- > Alan Mackenzie (Nuremberg, Germany). "A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2" certainly does have solutions, some of which Archie has given, but then he confuses himself with incorrect arithmatic so he's not sure. Considering his past history, the confusion will only grow with time.
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| From | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| Date | 2019-03-11 19:32 -0700 |
| Subject | Jennifer Wilson, Alex Wright, Lexing Ying, Xuwen Zhu, of Stanford Univ, are you as stupid as Eastside to never understand Real Proton = 840 MeV with electron= muon and .5MeV was Dirac magnetic monopole// ellipse is never a conic (see proof below) |
| Message-ID | <e29d23d3-8497-458f-9749-d960f789bd97@googlegroups.com> |
| In reply to | #436865 |
On Monday, March 11, 2019 at 12:02:35 PM UTC-5, eastsi...@gmail.com wrote: > but then he confuses himself with incorrect arithmatic so he's not sure. > Considering his past history, the confusion will only grow with time. Jennifer Wilson, Alex Wright, Lexing Ying, Xuwen Zhu, of Stanford Univ, are you as stupid as Eastside to never understand Real Proton = 840 MeV with electron= muon and .5MeV was Dirac magnetic monopole// ellipse is never a conic (see proof below) On Thursday, March 7, 2019 at 6:02:46 PM UTC-6, eastsi...@gmail.com wrote: > > Archie, ALL scientists know what causes summer and winter. Show me one who dossn't. NOBOBY suggests it because of Doppler redshift. OLGA K. DUDKO, RAPHAEL M. FLAUGER,MICHAEL M. FOGLER, of UC San Diego, are you as stupid as Eastside to never understand Real Proton = 840 MeV with electron= muon and .5MeV was Dirac magnetic monopole// ellipse is never a conic (see proof below) AP writes: Eastside a 5 year endless insane stalker, time for medication for Erik Eastside, instead of his senseless barking attack dog stunts .. .- " `-. ,..-''' ```....'`-.. , . `.' ' `. .' .' ` ` ' `.. ; . ; .' . `. ; ; . ' `. . ' . ' ` `. | . '. ' . 0 0 ' `. ' ` ; ` .' ` ; U ` ; '; ` : | ;.. :` ` : `;. ```. .-; | ' '. ` ``.., .' :' ' ; ` ;'.. ..-'' ' ' Hi, I'm the village idiot Erik Eastside, and although I gargle a few lines of meaningless math, I spend my time attacking those on sci.math who actually do math. I am a loser and life for me boils down to attack attack attack for I am a depressed worthless soul, and my parents won't give me the money to see a psychologists to help. So I have "no life" unless I can attack AP 24 -- 7 -- 365 ` ` ; ````'''""' ; ' ' ` ` ; ; ' ' ` ` ; ; ' ' ` `. ````'''''' ' ' ` . ' ' / ` `. ' ' . / ` .. ..' .'"""""...' / .` ` ``........-' .'` .....''' / .'' ; ` .' ` ...'.' ; .' ` .' ` "" .' .' | ` .; \ ` ; .' | `. . . . ' . \ ` :' | ' ` , `. ` | ' ` ' `. ` ` ' ` ; `. | `.' ` ; `-' `...' NNTP-Posting-Host: 64.201.118.229 From: eastsi...@gmail.com Stanford University, math dept. Gregory Brumfiel, Daniel Bump, Emmanuel Candès, Gunnar Carlsson, Moses Charikar, Sourav Chatterjee, Tom Church, Ralph Cohen, Brian Conrad, Brian Conrey, Amir Dembo, Persi Diaconis, Yakov Eliashberg, Robert Finn, Jacob Fox, Laura Fredrickson, Søren Galatius, George Schaeffer, Or Hershkovits, David Hoffman, Eleny Ionel, Renata Kallosh, Yitzhak Katznelson, Vladimir Kazeev, Michael Kemeny, Steven Kerckhoff, Susie Kimport, Jun Li, Tai-Ping Liu, Mark Lucianovic, Jonathan Luk, Frederick Manners, Rafe Mazzeo, James R. Milgram, Maryam Mirzakhani, Stefan Mueller, Christopher Ohrt, Donald Ornstein, George Papanicolaou, Lenya Ryzhik, Richard Schoen, Leon Simon, Rick Sommer, Kannan Soundararajan, Tadashi Tokieda, Cheng-Chiang Tsai, Ravi Vakil, András Vasy, Akshay Venkatesh, Jan Vondrák, Brian White, Wojciech Wieczorek, Jennifer Wilson, Alex Wright, Lexing Ying, Xuwen Zhu President: Marc Tessier-Lavigne (neuroscience) Provost: Persis Drell (physics) Stanford physics dept. Alexander Fetter, John Lipa, William Little, Douglas Osheroff, David Ritson, H. Alan Schwettman, John Turneaure, Robert Wagoner, Stanley Wojcicki, Mason Yearian CalTech math dept Michael Aschbacher, Alexei Borodin, Danny Calegari Matthias Flach, Anton N. Kapustin, Alexander Kechris Alexei Kitaev, Matilde Marcolli, Nikolai Makarov, Vladimir Markovic, Hiroshi Oguri, Eric Rains, Dinakar Ramakrishnan Barry Simon, Richard Wilson, Tom Graber, Sergei Gukov, Elena Mantovan, Yi NI, Caltech Physics Dept Barry Barish, Felix Boehm, Steven Frautschi Murray Gell-Mann, David Goodstein, Thomas Phillips, John Schwarz, Barry Simon, Kip Thorne, Petr Vogel, Rochus Vogt, Ward Whaling, Michael E. Brown, Konstantin Batygin UCLA chancellor: Gene D. Block (biology) UCLA Physics dept Ernest Abers, Elihu Abrahams, Katsushi Arisaka, Michalis Bachtis Eric Becklin, Zvi Bern, Rubin Braunstein, Stuart Brown, Robijn Bruinsma Charles Buchanan, Wesley Campbell, Troy Carter, Sudip Chakravarty W. Gilbert Clark, John Cornwall, Robert Cousins, Eric D'Hoker Robert Finkelstein, Christian Fronsdal, Walter Gekelman, Graciela Gelmini George Gruner, Michael Gutperle, Brad Hansen, Jay Hauser, Karoly Holczer Huan Huang, Eric Hudson, George Igo, Per Kraus, Alexander Kusenko Thomas Mason, George Morales, Warren Mori, Steven Moszkowski Christoph Niemann, Kumar Patel, Roberto Peccei, Claudio Pellegrini Seth Putterman, B. Regan, James Rosenzweig, Joseph Rudnick David Saltzberg, William Slater, Reiner Stenzel, Terry Tomboulis, Jean Turner Univ Calif San Diego, physics dept HENRY D. I. ABARBANEL, KAM S. ARNOLD, DANIEL P. AROVAS, RICHARD D. AVERITT, JULIO T. BARREIRO, DIMITRI N. BASOV, STEVEN BOGGS, JAMES G. BRANSON, ADAM J. BURGASSER, LEONID V. BUTOV, ALISON COIL,EVA-MARIA S. COLLINS, MAX (MASSIMILIANO) DI VENTRA, PATRICK H. DIAMOND, FRED C. DRISCOLL, DANIEL H. DUBIN, OLGA K. DUDKO, RAPHAEL M. FLAUGER,MICHAEL M. FOGLER, ALEX FRAÑÓ, GEORGE M. FULLER,DANIEL R GREEN, KIM GRIEST, BENJAMIN GRINSTEIN,ALEXANDER GROISMAN, TARUN GROVER, JORGE E. HIRSCH, MICHAEL HOLST, TERENCE T. HWA, KENNETH A. INTRILIGATOR, ELIZABETH JENKINS, SUCKJOON JUN, BRIAN KEATING, DUSAN KERES, DAVID KLEINFELD , QUINN M. KONOPACKY, ELENA F. KOSLOVER, JULIUS KUTI, TONGYAN LIN, ANEESH V. MANOHAR, M. BRIAN MAPLE, JOHN A. MCGREEVY, THOMAS W. MURPHY, KAIXUAN NI, MICHAEL L. NORMAN, THOMAS M. O'NEIL, HANS P. PAAR, MARK PADDOCK, JEREMIE PALACCI, TENIO POPMINTCHEV, WOUTER-JAN RAPPEL,KARIN M. SANDSTROM, IVAN K. SCHULLER, LU J. SHAM,VIVEK SHARMA, TATYANA O. SHARPEE, BRIAN SHOTWELL, OLEG SHPYRKO, ELIZABETH H SIMMONS,SUNIL K. SINHA, DOUGLAS E. SMITH, HARRY SUHL Math dept Univ Calif, San Diego Edward Bender, James Bunch, Thomas Enright, Ronald Evans, Jay Fillmore, Carl FitzGerald, Michael Freedman, Adriano Garsia, Fan Graham, Leonard Haff, Hubert Halkin, Richard Hamilton, Bill Helton, Jim Lin, Alfred Manaster, John O'Quigley, Yose Rinott, Burt Rodin, Murray Rosenblatt, Linda Rothschild, Michael Sharpe, Lance Small, Don Smith, Harold Stark, Audrey Terras, Adrian Wadsworth, Nolan Wallach, John Wavrik, Daniel Wulbert /\-------/\ \::O:::O::/ (::_ ^ _::) \_`-----'_/ You mean the classroom is the world, not just my cubbyhole in LA? And, even though you-- professors of physics/math, want to remain silent and stupid in Real Electron = muon, and true real Calculus with a geometry proof of Fundamental Theorem of Calculus, your students deserve better. Yes, there , what did they say--Which AP theory do they love the most, that real electron is the muon or the power of Sun and stars is not really fusion but is the Faraday Law inside of atoms creating monopoles and turning Space into energy that fuels the Sun and stars. My rough estimate is that fusion only supplies 10% or less of Sun and stars. But of course, I could not have discovered the true starpower when under the idiotic idea that the electron was a mere .5MeV when it truly is 105 MeV. What answer did they give? Proofs ellipse is never a conic, always a cylinder section by Archimedes Plutonium -------------------- AP's proof the ellipse is never a Conic Section, always a Cylinder section, and how the proof works Let us analyze AP's Proof On Friday, September 14, 2018 at 6:57:36 PM UTC-5, Archimedes Plutonium wrote: Array:: Analytic Geometry proof that Cylinder section= Ellipse//Conic section = Oval, never ellipse Now I did 3 Experiments and 3 models of the problem, but it turns out that one model is superior over all the other models. One model is the best of all. That model is where you construct a cone and a cylinder and then implant a circle inside the cone and cylinder attached to a handle so that you can rotate the circle inside. Mine uses a long nail that I poked holes into the side of a cylinder and another one inside a cone made from heavy wax paper of magazine covers. And I used a Mason or Kerr used lid and I attached them to the nail by drilling two holes into each lid and running a wire as fastener. All of this done so I can rotate or pivot the circle inside the cylinder and cone. You need a long nail, for if you make the models too small or too skinny, you lose clarity. ARRAY, Analytic Geometry Proof, Cylinder Section is a Ellipse:: E __ .-' `-. .' `. / \ ; ; | G c | H ; ; \ / `. .' `-. _____ .-' F Alright, focus on the distance from c to F in the cone-cut compared to the distance from c to E In a Cylinder cut, those two distances are the same because a cylinder has two axes of symmetry. The side view of a cylinder is this | | | | | | That allows cE to be the same distance as cF But the side view of the cone is /\E /c \ F / \ The distance c to E is shorter because the slant of the side walls of the cone are in the direction of shortening cE, whereas the slant opposite c in cF make that distance larger than cE The above is a view of a ellipse with center c and is produced by the Sectioning of a Cylinder as long as the cut is not perpendicular to the base, and as long as the cut involves two points not larger than the height of the cylinder walls. What we want to prove is that the cut is always a ellipse, which is a plane figure of two axes of symmetry with a Major Axis and Minor Axis and center at c. Side view of Cylinder EGFH above with entry point cut at E and exit point cut at F and where c denotes the central axis of the cylinder and where x denotes a circle at c parallel with the base-circle of cylinder | | | | E | | | | |x c |x | | | | | | |F | | | | | | | So we can see that the distance cE = cF in cylinder for the walls are Parallel to one another, giving distance symmetry But in the Cone, the walls are not parallel, shortening the distance cE compared to cF. Leaving only one axis of symmetry that of EF. The oval is the conic section of a cut at a slant, while the cylinder cut at a slant is a ellipse. The Oval has just one axis of symmetry. So, what is the proof that figure EGFH is always an ellipse in the cylinder section? The line segment GH is the diameter of the circle base of cylinder and the cylinder axis cuts this diameter in half such that Gc = cH. Now we only need to show that Fc = cE. This is done from the right triangles cxF and cxE, for we note that by Angle-Side-Angle these two right triangles are congruent and hence Fc = cE, our second axis of symmetry and thus figure EGFH is always an ellipse. QED Array proof:: Analytic Geometry proof that Conic section= Oval// never ellipse ARRAY, Analytic Geometry Proof, Conic Section is a Oval, never an ellipse:: A ,'" "`. / \ C | c | D \ / ` . ___ .' B The above is a view of a figure formed from the cut of a conic with center c as the axis of the cone and is produced by the Sectioning of a Cone as long as the cut is not perpendicular to the base, and as long as the cut is not a hyperbola, parabola or circle (nor line). What we want to prove is that this cut is always a oval, never an ellipse. An oval is defined as a plane figure of just one axis of symmetry and possessing a center, c, with a Major Diameter as the axis of symmetry and a Minor Diameter. In our diagram above, the major diameter is AB and minor diameter is CD. Alright, almost the same as with Cylinder section where we proved the center was half way between Major Axis and Minor Axis of cylinder, only in the case of the Conic, we find that the center is half way between CD the Minor Diameter, but the center is not halfway in between the Major Diameter, and all of that because of the reason the slanted walls of the cone cause the distance cA to be far smaller than the distance cB. In the diagram below we have the circle of x centered at c and parallel to base. The angle at cx is not 90 degrees as in cylinder. The angle of cAx is not the same as the angle cBx, as in the case of the cylinder, because the walls of the cone-for line segments- are slanted versus parallel in the cylinder. Triangles cAx and cBx are not congruent, and thus, the distance of cA is not equal to cB, leaving only one axis of symmetry AB, not CD. / \A x/ c \x B/ \ Hence, every cut in the Cone, not a hyperbola, not a parabola, not a circle (not a line) is a Oval, never an ellipse. QED --Archimedes Plutonium AP Very crude dot picture of 5f6, 94TH ELECTRON=muon DOT CLOUD of 231Pu ::\ ::|:: /:: ::\::|::/:: _ _ (:Y:) - - ::/::|::\:: ::/ ::|:: \:: One of those dots is the Milky Way galaxy. And each dot represents another galaxy. . \ . . | . /. . . \. . .|. . /. . ..\....|.../... ::\:::|::/:: --------------- ------------- --------------- (Y) ------------- --------------- -------------- ::/:::|::\:: ../....|...\... . . /. . .|. . \. . . / . . | . \ . http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers. Read my recent posts in peace and quiet. https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe Archimedes Plutonium
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| From | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| Date | 2019-03-11 20:24 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <926aceaf-20b9-4aef-b3cf-bbefb0fd8318@googlegroups.com> |
| In reply to | #436803 |
On Monday, March 11, 2019 at 12:23:59 AM UTC-5, Archimedes Plutonium wrote: > > 4^4 + 4^4 = 8^3 which has a nonprime factor of 4 > > > > So, all I need to do, is show that (kA)^x + (kB)^y = (kC)^z is just a more fancy and complicated Pythagorean theorem based upon 2 + 2 = 2^2 = 4 > Yes, I think all I need to do to prove Generalized FLT (kA)^x + (kB)^y = (kC)^z is show that 2 + 2 = 2*2 = 4 is a linear vector space increase by factor k forming a solution For example 7^3 + 7^4 = ??? involves a linear vector with 7 as a factor 14^3 Because 2 + 2 has a solution of 2*2 as a linear vector we have (3,4,5) as solution set So we take the prime 5 and it must have a solution set of form (5kA)^x + (5jB)^y = (5hC)^z AP
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| From | Mike Hart <gmoralesor@gmail.com> |
|---|---|
| Date | 2019-03-12 05:44 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <eb8ba3ac-a4a8-42d5-b0d6-6191db7f92a8@googlegroups.com> |
| In reply to | #436923 |
AP, I think you are overcomplicating things. Proving this equation has a solution is far easier than what you are doing...
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| From | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| Date | 2019-03-12 12:01 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <b39c85aa-8df4-406a-a47d-0b89739df7ba@googlegroups.com> |
| In reply to | #436965 |
Yes, i agree. That proving A^x + B^y = C^z has solutions, comes easily from the observation of 2 + 2 = 2^2 = 4 as a vector multiplication algebra. 2^3 + 2^3 = 2^4 is a vector multiplication of 2+ 2 = 2^2 As is all solutions of A^x + B^y= C^z AP
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| From | Mike Hart <gmoralesor@gmail.com> |
|---|---|
| Date | 2019-03-12 12:11 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <8ddc13ca-c6da-46ed-b0a1-5b5a33b19698@googlegroups.com> |
| In reply to | #437011 |
And then, what are you trying to prove?
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| From | eastside.erik@gmail.com |
|---|---|
| Date | 2019-03-12 12:14 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <a1af7694-6ca8-466e-a9cb-ebbf5ccfb8de@googlegroups.com> |
| In reply to | #437011 |
On Tuesday, March 12, 2019 at 12:01:31 PM UTC-7, Archimedes Plutonium wrote: > Yes, i agree. That proving A^x + B^y = C^z has solutions, comes easily from the observation of 2 + 2 = 2^2 = 4 as a vector multiplication algebra. > > 2^3 + 2^3 = 2^4 is a vector multiplication of 2+ 2 = 2^2 > > As is all solutions of A^x + B^y= C^z > > AP So is has solutions. So what?
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| From | Archimedes Plutonium <plutonium.archimedes@gmail.com> |
|---|---|
| Date | 2019-03-12 12:30 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <37df792f-a273-4388-9583-310864292b21@googlegroups.com> |
| In reply to | #437011 |
And now within this Vector Space proof of Generalized FLT is a pattern that also needs being fully revealed of its algebra mechanism. 2^3 + 2^3 = 2^4 with prime divisor 2 3^3 + 6^3 = 3^5 with prime divisor 3 7^3 + 7^4 = 14^3 with prime divisor 7 The first is the smallest solution for prime 2 Second is smallest for prime 3 Next is smallest prime 7 What we have missing is smallest for prime 5– anyone have the smallest prime 5 solution set? Then we probably can construct a formula or rule that picks up in a orderly pattern the smallest prime 11, 13, 17, etc etc Such a formula would unlock some secrets of how Vector Space multiplication and addition works. Fun stuff,, eh,,, for breakfast,,, AP
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| From | Mike Hart <gmoralesor@gmail.com> |
|---|---|
| Date | 2019-03-12 13:50 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <a54bc273-fa2a-427f-876f-69d6fd33c02f@googlegroups.com> |
| In reply to | #437014 |
You are not going to say what you are trying to prove, are you? ~_~
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| From | eastside.erik@gmail.com |
|---|---|
| Date | 2019-03-12 15:40 -0700 |
| Subject | Re: proving both Pythagorean theorem along with Generalized FLT all from pure algebra of 2^1 + 2^1 = 2^2 |
| Message-ID | <6151d0a4-1069-4ce7-bd50-3d96566ebc44@googlegroups.com> |
| In reply to | #437014 |
On Tuesday, March 12, 2019 at 12:30:49 PM UTC-7, Archimedes Plutonium wrote: > And now within this Vector Space proof of Generalized FLT is a pattern that also needs being fully revealed of its algebra mechanism. > > > 2^3 + 2^3 = 2^4 with prime divisor 2 > 3^3 + 6^3 = 3^5 with prime divisor 3 > 7^3 + 7^4 = 14^3 with prime divisor 7 > > The first is the smallest solution for prime 2 > > Second is smallest for prime 3 > > Next is smallest prime 7 > > What we have missing is smallest for prime 5– anyone have the smallest prime 5 solution set? > > Then we probably can construct a formula or rule that picks up in a orderly pattern the smallest prime 11, 13, 17, etc etc > > Such a formula would unlock some secrets of how Vector Space multiplication and addition works. > > Fun stuff,, eh,,, for breakfast,,, > > AP So you have no idea what you're trying to prove. OK.
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| From | moroney@world.std.spaamtrap.com (Michael Moroney) |
|---|---|
| Date | 2019-03-10 17:08 +0000 |
| Subject | Re: Archimedes "just not bolted down too tight in the first place" Plutonium flunked the physics lifetime-generation test |
| Message-ID | <q63gak$mt0$3@pcls7.std.com> |
| In reply to | #436723 |
AlzheimerPlutonium <plutonium.archimedes@gmail.com> fails at math and science: >For once we scoot over the galaxies, we get them forming the surface of a >cylinder or a coil of wire in Faraday Law. "We" again, Archie? Could you explain how your diseased cats could have an opinion on galaxies or the Faraday Law? x-no-archive: yes
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| From | j4n bur53 <janburse@fastmail.fm> |
|---|---|
| Date | 2019-03-10 21:00 +0100 |
| Message-ID | <q63qdl$for$1@news.albasani.net> |
| In reply to | #436507 |
AP brain farto writes, his microgram brain
only needs a small wheelchair:
|_
| |
* *
And not:
|
|__
| |
| |
o o
Archimedes Plutonium schrieb:
> Below is my 2014 Proof of both Generalized FLT and Regular FLT, where the Regular falls out as a corollary consequence. The reason for this update is that there are clarity issues going from Generalized FLT proof to arriving at a proof of Regular FLT. Too many puzzled heads and minds as to how Regular FLT is a direct consequence of Generalized FLT. In this regard, I bend over backwards to give that clarity.
>
> --- 2014, 2016 writings ---
>
>
> AP PROOF OF BOTH GENERALIZED FLT AND REGULAR FLT
>
> My history of this proof below began 2014
> Generalized FLT date of discovery 2014
> by Archimedes Plutonium
> Newsgroups: sci.math
> Date: Wed, 8 Jan 2014 02:32:14 -0800 (PST)
> Complaints-To: groups...@google.com
> Injection-Info: glegroupsg2000goo.googlegroups.com; posting-host=166.137.110.8;
> posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd
> NNTP-Posting-Host: 166.137.110.8
> User-Agent: G2/1.0
> MIME-Version: 1.0
> Message-ID: <0930d831-785f-4440-bf56-132cc17c5707@googlegroups.com>
> Subject: taking on both FLT and (sic) Generalized FLT in one proof; using Condensed Rectangles
> #1388 Correcting Math
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Wed, 08 Jan 2014 10:32:14 +0000
>
> My proof of FLT turned out not to be easy for High School. Easy for College mid level, not High School.
>
> For the umpteenth time below is my FLT
>
> Well the sci.math has a complete history of my adventures with Fermat's Last Theorem starting with August 1993, and developing many twists and turns. Several times I had to throw out my prior attempts.
>
> What emerged was decades later, a final true proof of FLT. It has one huge starting surprise to it. Hugely Startling Surprise. The surprise is that a class of math proofs cannot be proven until a "more general theorem that overlays the "lesser theorem tucked away inside" the more general theorem is proven FIRST"
>
> So that-- there never exists a proof of FLT until you first prove true the Generalized FLT
>
> What is Generalized FLT? Glad you asked, for it is:
>
> A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2
>
> FLT is of course
>
> A^n + B^n = C^n where A,B,C, n are positive integers and n is greater than 2
>
> Newsgroups: sci.math
> Date: Thu, 9 Jun 2016 13:38:48 -0700 (PDT)
>
> Subject: Proof of Generalized FLT & Fermat's Last Theorem #178 Correcting Math 4th ed
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Thu, 09 Jun 2016 20:38:49 +0000
>
>
> Proof of Generalized FLT & Fermat's Last Theorem #178 Correcting Math 4th ed
>
>
> PROOFS of Generalized FLT & FERMAT's LAST THEOREM as corollary
>
> Editing and commentary corner: Once Generalized FLT and FLT are turned into a geometrical perspective-- condensed rectangles, then the proof is as easy as making homemade cherry pie. And the importance of proving Generalized FLT first is that FLT never has a proof until Generalized FLT is proven first.
>
> Summary of text: Both proofs of Generalized FLT and FLT are based on a fact of geometry, that you can represent a number with its cofactors as the sides of a rectangle. And to prove either Generalized FLT or FLT is a simple matter of stacking two rectangles that have equal sides, A and B to produce a third rectangle C which has a side equalling the _shared side_ of A and B.
>
> TEXT:
>
> I decided I needed to stiffen up the proof of Generalized FLT below. To a logical person, they often streamline their proofs and do not bother with adding some information which people not used to logic have a difficult time in seeing. For me, it is redundant to include the distributive law into the proof of Generalized FLT, but to those who do not do math but only on occasion, they would not see the logic unless I explain those very details. So below is a more stiffened up proof of Generalized FLT.
>
> Proof of the Generalized FLT conjecture that proves Fermat's Last Theorem
>
> What is Generalized FLT? Glad you asked, for it is:
>
> A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2
>
> FLT is of course
>
> A^n + B^n = C^n where A,B,C, n are positive integers and n is greater than 2
>
> I proved Generalized FLT and FLT (Fermat's Last Theorem) before I discovered that Logical Material Implication Table of T,F,T,T is incorrect and should be that of T,F,undefined, undefined. What this does is remove reductio ad absurdum as a mathematics proof technique as only a probability technique and no longer a deduction. It means the only valid proof method for mathematics, is construction proofs. My Generalized FLT and FLT are construction proofs. Another feature of the true Logic Implication operator, is that corollaries of mathematics cannot be proven as "stand alone conjectures". And that a corollary requires the over-arching- theorem attending the corollary be proven beforehand. This implies that Wiles's FLT is not true for in order to truly prove FLT, a proof of Generalized FLT had to come first.
>
> We see the relationship between a Theorem and its Corollary very easily from Generalized FLT and FLT, in that we have all these cases to worry about. The history of FLT was a case study, prove it in the case of exponent this and that, but never a proof of all of FLT, and that is because corollaries are never proven as stand alone theorems and must have their theorem (Generalized FLT) proven first. This is because Logic Implication is not T,F,T,T where false proofs hide behind those last two T, T when they should be undefined, undefined. The reason Implication must be T,F,undefined, undefined is because mathematics has 2/0 and 0/0 where division by 0 is undefined, and that Old Logic with its T,F,T,T does not allow for division by zero.
>
> Detailed Proofs Generalized FLT conjecture with its FLT corollary
>
>
> Both proofs of Generalized FLT and FLT are based on a fact of geometry, that you can represent a number with its cofactors as the sides of a rectangle. And to prove either Generalized FLT or FLT is a simple matter of stacking two rectangles that have equal sides, A and B to produce a third rectangle C which has a side equalling the _shared side_ of A and B.
> ________________________
> DETAILED PROOF OF Generalized FLT
> ________________________
>
> It is a constructive proof.
>
> We make the table of all the numbers possible in the Generalized FLT Conjecture as the conglomeration of exponents of 3 or larger as this set:
>
> {1, 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, . .}
>
> Here we have conglomerated exp3 and exp4 and exp5 etc etc into one set.
>
> We know Generalized FLT has solutions of A+B=C in that set for here are three examples:
>
> 2^3 + 2^3 = 2^4 with prime divisor 2
> 3^3 + 6^3 = 3^5 with prime divisor 3
> 7^3 + 7^4 = 14^3 with prime divisor 7
>
> What we need to prove is that all solutions have a prime divisor in common, ie all three rectangles of A, B, C so that A+B=C, have one shared side equal to one another.
>
> Definition of Condensed-Rectangle: given any number in the set of conglomerated exponents, we construct rectangles of that number from its unit squares whose sides are cofactors of the number. For instance, rectangle of 216 units as either 12x18 units, or 9x24 units, or 6x36 units or 3x72 units, or 2x108, but never a 1x216 units. We exclude 1 times the number as a condensed rectangle. So a condensed-rectangle is one in which it is composed of cofactors of the number in question, except for 1, and the number itself for 1x216 units is not a condensed-rectangle.
>
> Now for the constructive proof that Generalized FLT solutions must have a common prime divisor.
>
> We stack Condensed-Rectangles of the number-space that Generalized FLT conjecture applies:
>
> Solution Number Space for Generalized FLT now becomes these condensed-rectangles:
>
> { 2*4, 2*8, 4*4, 3*9, 2*16, 4*8, 2*32, 4*16, 8*8,. . . }
>
> We convert each of those numbers into Condensed-Rectangle, except 1 of course, and where many numbers have several condensed rectangles so the Solution Space of Numbers increases by a large amount. If an A and B as condensed-rectangles have the same side such as 3x9 units and 9x24units
> wherein you stack them on their shared side of 9 and which matches another number of its condensed-rectangle such as 9x27 units, then you have a Generalized FLT solution of A+B=C. For if we were to take the 9 by 27 condensed rectangle it decomposes into 3x9 and 9x24.
>
> Now, the question is, are all A+B equal to a C, form stacked condensed rectangles that share a common side?
>
> All stackable condensed-rectangles must have one side the same for the two rectangles to stack, in the case above it is the side 9 with its common divisor of the prime 3.
>
> If any other solution to Generalized FLT had A stacked upon B without a common side between them, then the figure formed cannot be a overall new rectangle but something that looks like this:
>
> HHHHHH
> HHHHHH
> HHHHHHHHHH
> HHHHHHHHHH
>
> That is not a condensed rectangle and all the numbers of the Solution Space, except the number 1, are condensed rectangles. That above figure is 6-sided figure. That is a 6-sided figure, yet a rectangle is only a 4 sided figure. That is not a Condensed Rectangle, represented by its cofactors. So that equality can not be achieved by any other stacking than condensed rectangles equalling condensed rectangles.
>
> Then the question is, can we have an A and B with a shared common side equal to a C that is a condensed rectangle with no common side shared with A and B?
>
> The question is, how can I be sure that all the A, B, C such that A + B = C have a common prime divisor?
>
> As if the question is asking whether the Condensed Rectangles covered the question by forbidding any equality unless there is a common shared side in A in B and in C.
>
> Well, the answer is easily enough covered for the Condensed Rectangles eliminates any possibility of A,B,C where A+B = C and not have a shared side by all three of A, B, C. It does this by the Distributive law of integers.
>
> All the numbers in the solution space of Generalized FLT have condensed rectangles, except the number 1.
>
> All the A, B, C are written as condensed rectangles of (s*t) + (r*p) = (u*v).
>
> For example (9*3) + (9*24) = (9*27) which is 3^3 + 6^3 = 3^5 which is 27 + 216 = 243.
>
> In order for (s*t) + (r*p) = (u*v) then the s, r, u have to be equal sides. Have to be (9*t) + (9*p) = (9*v) in the example of 27 + 216 = 243.
>
> Distributive Law (9*3)/9 + (9*24)/9 = (9*27)/9 where 3 + 24 = 27
>
> So, give me three numbers A, B, C, chosen arbitrarily from the Solution Space of Generalized FLT {1, 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, . .} except of course 1, and can those three chosen arbitrarily A, B, C obey A + B = C? Only if they obey the Distributive Law can the A + B equal to the C when we write the A, B, C as condensed rectangles.
>
> QED
>
>
> _________________________________________
> Detailed Proof of FLT using condensed-rectangles
> _________________________________________
>
> It is a construction proof method for we show that it is impossible to construct A+B = C inside of a specific exponent.
>
> Fermat's Last Theorem FLT conjecture says there are no solutions to the equation a^y + b^y = c^y where a,b,c,y are positive integers and y is greater than 2.
>
> The number Space that governs FLT is this:
>
> exp3 {1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, . .}
>
> exp4 {1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, . .}
>
> exp5 {1, 32, 243, 1024, 3125, 7776, 16807, 32,768, 59,049, 100,000, 161,051, 248,832, 371,293, . .}
>
> exp6 .....
> .
> .
> .
> .
>
> So in FLT we ask whether there are any triples, A,B,C in any one of those _specific exponents_ such that A+B=C. In FLT, our solution space is only one particular exponent such as 3 or 4, or 5 to hunt down and find a A,B,C to satisfy A+B=C.
>
> In the proof we use Condensed-Rectangles which is defined as a rectangle composed of unit squares of the cofactors of a number, except for 1 x number itself. So the number 27 in exp3 has Condensed Rectangles of 3x9 only. The number 125 in exp3 has condensed rectangles of 5x25 only, and the number 81 in exp4 has condensed rectangles of 3x27 and 9x9.
>
> Now in the proof of Generalized FLT solutions of A + B = C require a common divisor.
>
> 2^3 + 2^3 = 2^4 with prime divisor 2
> 3^3 + 6^3 = 3^5 with prime divisor 3
> 7^3 + 7^4 = 14^3 with prime divisor 7
>
> Here in FLT, we need not even worry about exponents because all solutions to Generalized FLT encompass exponents so that if these were FLT solutions:
>
> 2^? + 2^? = 2^? with prime divisor 2
> 3^? + 6^? = 3^? with prime divisor 3
> 7^? + 7^? = 14^? with prime divisor 7
>
> So in that construction of a solution to FLT there is a common divisor and so now we divide the equation by the common divisor, and we get this:
>
> 1^y + 1^y = 1^y
> 1^z + 2^z = 1^z
> 1^w + 1^w = 2^w
>
> And those are impossible constructions. So the proof of FLT requires Generalized FLT be proven first in order to display that a Generalized FLT proof cannot co-exist unless FLT has no solutions.
>
> Now this is the moment in 2019 where I like to make that more clear. For there are many puzzled and scratching heads of thinking on how that Generalized FLT so easily proves Regular FLT. Let me write it as clear as possible.
>
> So in Generalized FLT to prove Regular FLT we can easily do that by saying all solutions have a prime factor. Suppose a Regular FLT solution set exists, then it has a prime factor. So, multiply that prime factor --out-- yes, multiply it out, AND BECAUSE OF THAT ALGEBRA AXIOM I WAS PLAYING WITH, that multiplied out factor would also have to be a solution set-- and keep multiplying out by constant k, but then you reach a point where you have no prime factor and cannot be a solution due to Generalized FLT. It cannot be a solution because it has no prime factor, and Generalized FLT says -- All Solutions have a prime factor. Contradictory to the axiom that every multiplication by k is a solution to A^k + B^k = C^k
>
> Let me show you the above by a numbers example.
>
> 12^2 + 16^2 = 20^2 has prime factor 2 so divide out the prime factor leaves 6^2 + 8^2 = 10^2 which has another prime factor of 2 divide it out leaves 3^2 + 4^2 = 5^2 and here we no longer have a prime factor. This example shows that Axiom of Algebra, that you can always retain equality with any constant number k as (kA)^2 + (kB)^2 = (kC)^2. Try it out yourself by plugging in for k any whole number or any fraction and you preserve equality.
>
> So Generalized says that if we have a solution 12^2 + 16^2 = 20^2 we can divide out the solution by the prime factor which is 2 in our sample. But the question is-- can the equation remaining be a solution? And yes of course 6^2 + 8^2 = 10^2 but if it is a solution, it must be able to be divided out by a prime factor by Generalized. And this chain of events eventually comes down to where you can no longer have a prime factor 3^2 + 4^2 = 5^2. And Generalized demands always, every solution have a prime factor. So here we have a impossibility or as mathematicians like to call it-- a Contradiction. Thus, the idea of a Regular FLT having a solution set conflicts and contradicts what was proven by Generalized FLT. That means a Regular FLT can never have a solution set. QED
>
> Very crude dot picture of 5f6, 94TH
> ELECTRON DOT CLOUD of 231Pu
>
>
> ::\ ::|:: /::
> ::\::|::/::
> _ _
> (:Y:)
> - -
> ::/::|::\::
> ::/ ::|:: \::
>
> One of those dots is the Milky Way galaxy. And
> each dot represents another galaxy.
>
>
> . \ . . | . /.
> . . \. . .|. . /. .
> ..\....|.../...
> ::\:::|::/::
> --------------- -------------
> --------------- (Y) -------------
> --------------- --------------
> ::/:::|::\::
> ../....|...\...
> . . /. . .|. . \. .
> . / . . | . \ .
>
>
> http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
>
> I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
>
> https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
> Archimedes Plutonium
>
[toc] | [prev] | [next] | [standalone]
| From | j4n bur53 <bursejan@gmail.com> |
|---|---|
| Date | 2019-03-17 12:31 -0700 |
| Message-ID | <cf9920b6-cbdf-465b-8952-79a9436c1054@googlegroups.com> |
| In reply to | #436507 |
I guess its a micro micro brain,
so this chair already works for AP brain farto:
h
On Thursday, March 7, 2019 at 6:45:17 AM UTC+1, Archimedes Plutonium wrote:
> Below is my 2014 Proof of both Generalized FLT and Regular FLT, where the Regular falls out as a corollary consequence. The reason for this update is that there are clarity issues going from Generalized FLT proof to arriving at a proof of Regular FLT. Too many puzzled heads and minds as to how Regular FLT is a direct consequence of Generalized FLT. In this regard, I bend over backwards to give that clarity.
>
> --- 2014, 2016 writings ---
>
>
> AP PROOF OF BOTH GENERALIZED FLT AND REGULAR FLT
>
> My history of this proof below began 2014
> Generalized FLT date of discovery 2014
> by Archimedes Plutonium
> Newsgroups: sci.math
> Date: Wed, 8 Jan 2014 02:32:14 -0800 (PST)
> Complaints-To: groups...@google.com
> Injection-Info: glegroupsg2000goo.googlegroups.com; posting-host=166.137.110.8;
> posting-account=fsC03QkAAAAwkSNcSEKmlcR-W_HNitEd
> NNTP-Posting-Host: 166.137.110.8
> User-Agent: G2/1.0
> MIME-Version: 1.0
> Message-ID: <0930d831-785f-4440-bf56-132cc17c5707@googlegroups.com>
> Subject: taking on both FLT and (sic) Generalized FLT in one proof; using Condensed Rectangles
> #1388 Correcting Math
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Wed, 08 Jan 2014 10:32:14 +0000
>
> My proof of FLT turned out not to be easy for High School. Easy for College mid level, not High School.
>
> For the umpteenth time below is my FLT
>
> Well the sci.math has a complete history of my adventures with Fermat's Last Theorem starting with August 1993, and developing many twists and turns. Several times I had to throw out my prior attempts.
>
> What emerged was decades later, a final true proof of FLT. It has one huge starting surprise to it. Hugely Startling Surprise. The surprise is that a class of math proofs cannot be proven until a "more general theorem that overlays the "lesser theorem tucked away inside" the more general theorem is proven FIRST"
>
> So that-- there never exists a proof of FLT until you first prove true the Generalized FLT
>
> What is Generalized FLT? Glad you asked, for it is:
>
> A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2
>
> FLT is of course
>
> A^n + B^n = C^n where A,B,C, n are positive integers and n is greater than 2
>
> Newsgroups: sci.math
> Date: Thu, 9 Jun 2016 13:38:48 -0700 (PDT)
>
> Subject: Proof of Generalized FLT & Fermat's Last Theorem #178 Correcting Math 4th ed
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Thu, 09 Jun 2016 20:38:49 +0000
>
>
> Proof of Generalized FLT & Fermat's Last Theorem #178 Correcting Math 4th ed
>
>
> PROOFS of Generalized FLT & FERMAT's LAST THEOREM as corollary
>
> Editing and commentary corner: Once Generalized FLT and FLT are turned into a geometrical perspective-- condensed rectangles, then the proof is as easy as making homemade cherry pie. And the importance of proving Generalized FLT first is that FLT never has a proof until Generalized FLT is proven first.
>
> Summary of text: Both proofs of Generalized FLT and FLT are based on a fact of geometry, that you can represent a number with its cofactors as the sides of a rectangle. And to prove either Generalized FLT or FLT is a simple matter of stacking two rectangles that have equal sides, A and B to produce a third rectangle C which has a side equalling the _shared side_ of A and B.
>
> TEXT:
>
> I decided I needed to stiffen up the proof of Generalized FLT below. To a logical person, they often streamline their proofs and do not bother with adding some information which people not used to logic have a difficult time in seeing. For me, it is redundant to include the distributive law into the proof of Generalized FLT, but to those who do not do math but only on occasion, they would not see the logic unless I explain those very details. So below is a more stiffened up proof of Generalized FLT.
>
> Proof of the Generalized FLT conjecture that proves Fermat's Last Theorem
>
> What is Generalized FLT? Glad you asked, for it is:
>
> A^x + B^y = C^z where A,B,C,x,y,z are positive integers with x,y,z greater than 2
>
> FLT is of course
>
> A^n + B^n = C^n where A,B,C, n are positive integers and n is greater than 2
>
> I proved Generalized FLT and FLT (Fermat's Last Theorem) before I discovered that Logical Material Implication Table of T,F,T,T is incorrect and should be that of T,F,undefined, undefined. What this does is remove reductio ad absurdum as a mathematics proof technique as only a probability technique and no longer a deduction. It means the only valid proof method for mathematics, is construction proofs. My Generalized FLT and FLT are construction proofs. Another feature of the true Logic Implication operator, is that corollaries of mathematics cannot be proven as "stand alone conjectures". And that a corollary requires the over-arching- theorem attending the corollary be proven beforehand. This implies that Wiles's FLT is not true for in order to truly prove FLT, a proof of Generalized FLT had to come first.
>
> We see the relationship between a Theorem and its Corollary very easily from Generalized FLT and FLT, in that we have all these cases to worry about. The history of FLT was a case study, prove it in the case of exponent this and that, but never a proof of all of FLT, and that is because corollaries are never proven as stand alone theorems and must have their theorem (Generalized FLT) proven first. This is because Logic Implication is not T,F,T,T where false proofs hide behind those last two T, T when they should be undefined, undefined. The reason Implication must be T,F,undefined, undefined is because mathematics has 2/0 and 0/0 where division by 0 is undefined, and that Old Logic with its T,F,T,T does not allow for division by zero.
>
> Detailed Proofs Generalized FLT conjecture with its FLT corollary
>
>
> Both proofs of Generalized FLT and FLT are based on a fact of geometry, that you can represent a number with its cofactors as the sides of a rectangle. And to prove either Generalized FLT or FLT is a simple matter of stacking two rectangles that have equal sides, A and B to produce a third rectangle C which has a side equalling the _shared side_ of A and B.
> ________________________
> DETAILED PROOF OF Generalized FLT
> ________________________
>
> It is a constructive proof.
>
> We make the table of all the numbers possible in the Generalized FLT Conjecture as the conglomeration of exponents of 3 or larger as this set:
>
> {1, 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, . .}
>
> Here we have conglomerated exp3 and exp4 and exp5 etc etc into one set.
>
> We know Generalized FLT has solutions of A+B=C in that set for here are three examples:
>
> 2^3 + 2^3 = 2^4 with prime divisor 2
> 3^3 + 6^3 = 3^5 with prime divisor 3
> 7^3 + 7^4 = 14^3 with prime divisor 7
>
> What we need to prove is that all solutions have a prime divisor in common, ie all three rectangles of A, B, C so that A+B=C, have one shared side equal to one another.
>
> Definition of Condensed-Rectangle: given any number in the set of conglomerated exponents, we construct rectangles of that number from its unit squares whose sides are cofactors of the number. For instance, rectangle of 216 units as either 12x18 units, or 9x24 units, or 6x36 units or 3x72 units, or 2x108, but never a 1x216 units. We exclude 1 times the number as a condensed rectangle. So a condensed-rectangle is one in which it is composed of cofactors of the number in question, except for 1, and the number itself for 1x216 units is not a condensed-rectangle.
>
> Now for the constructive proof that Generalized FLT solutions must have a common prime divisor.
>
> We stack Condensed-Rectangles of the number-space that Generalized FLT conjecture applies:
>
> Solution Number Space for Generalized FLT now becomes these condensed-rectangles:
>
> { 2*4, 2*8, 4*4, 3*9, 2*16, 4*8, 2*32, 4*16, 8*8,. . . }
>
> We convert each of those numbers into Condensed-Rectangle, except 1 of course, and where many numbers have several condensed rectangles so the Solution Space of Numbers increases by a large amount. If an A and B as condensed-rectangles have the same side such as 3x9 units and 9x24units
> wherein you stack them on their shared side of 9 and which matches another number of its condensed-rectangle such as 9x27 units, then you have a Generalized FLT solution of A+B=C. For if we were to take the 9 by 27 condensed rectangle it decomposes into 3x9 and 9x24.
>
> Now, the question is, are all A+B equal to a C, form stacked condensed rectangles that share a common side?
>
> All stackable condensed-rectangles must have one side the same for the two rectangles to stack, in the case above it is the side 9 with its common divisor of the prime 3.
>
> If any other solution to Generalized FLT had A stacked upon B without a common side between them, then the figure formed cannot be a overall new rectangle but something that looks like this:
>
> HHHHHH
> HHHHHH
> HHHHHHHHHH
> HHHHHHHHHH
>
> That is not a condensed rectangle and all the numbers of the Solution Space, except the number 1, are condensed rectangles. That above figure is 6-sided figure. That is a 6-sided figure, yet a rectangle is only a 4 sided figure. That is not a Condensed Rectangle, represented by its cofactors. So that equality can not be achieved by any other stacking than condensed rectangles equalling condensed rectangles.
>
> Then the question is, can we have an A and B with a shared common side equal to a C that is a condensed rectangle with no common side shared with A and B?
>
> The question is, how can I be sure that all the A, B, C such that A + B = C have a common prime divisor?
>
> As if the question is asking whether the Condensed Rectangles covered the question by forbidding any equality unless there is a common shared side in A in B and in C.
>
> Well, the answer is easily enough covered for the Condensed Rectangles eliminates any possibility of A,B,C where A+B = C and not have a shared side by all three of A, B, C. It does this by the Distributive law of integers.
>
> All the numbers in the solution space of Generalized FLT have condensed rectangles, except the number 1.
>
> All the A, B, C are written as condensed rectangles of (s*t) + (r*p) = (u*v).
>
> For example (9*3) + (9*24) = (9*27) which is 3^3 + 6^3 = 3^5 which is 27 + 216 = 243.
>
> In order for (s*t) + (r*p) = (u*v) then the s, r, u have to be equal sides. Have to be (9*t) + (9*p) = (9*v) in the example of 27 + 216 = 243.
>
> Distributive Law (9*3)/9 + (9*24)/9 = (9*27)/9 where 3 + 24 = 27
>
> So, give me three numbers A, B, C, chosen arbitrarily from the Solution Space of Generalized FLT {1, 8, 16, 27, 32, 64, 81, 125, 128, 216, 243, 256, . .} except of course 1, and can those three chosen arbitrarily A, B, C obey A + B = C? Only if they obey the Distributive Law can the A + B equal to the C when we write the A, B, C as condensed rectangles.
>
> QED
>
>
> _________________________________________
> Detailed Proof of FLT using condensed-rectangles
> _________________________________________
>
> It is a construction proof method for we show that it is impossible to construct A+B = C inside of a specific exponent.
>
> Fermat's Last Theorem FLT conjecture says there are no solutions to the equation a^y + b^y = c^y where a,b,c,y are positive integers and y is greater than 2.
>
> The number Space that governs FLT is this:
>
> exp3 {1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, . .}
>
> exp4 {1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, . .}
>
> exp5 {1, 32, 243, 1024, 3125, 7776, 16807, 32,768, 59,049, 100,000, 161,051, 248,832, 371,293, . .}
>
> exp6 .....
> .
> .
> .
> .
>
> So in FLT we ask whether there are any triples, A,B,C in any one of those _specific exponents_ such that A+B=C. In FLT, our solution space is only one particular exponent such as 3 or 4, or 5 to hunt down and find a A,B,C to satisfy A+B=C.
>
> In the proof we use Condensed-Rectangles which is defined as a rectangle composed of unit squares of the cofactors of a number, except for 1 x number itself. So the number 27 in exp3 has Condensed Rectangles of 3x9 only. The number 125 in exp3 has condensed rectangles of 5x25 only, and the number 81 in exp4 has condensed rectangles of 3x27 and 9x9.
>
> Now in the proof of Generalized FLT solutions of A + B = C require a common divisor.
>
> 2^3 + 2^3 = 2^4 with prime divisor 2
> 3^3 + 6^3 = 3^5 with prime divisor 3
> 7^3 + 7^4 = 14^3 with prime divisor 7
>
> Here in FLT, we need not even worry about exponents because all solutions to Generalized FLT encompass exponents so that if these were FLT solutions:
>
> 2^? + 2^? = 2^? with prime divisor 2
> 3^? + 6^? = 3^? with prime divisor 3
> 7^? + 7^? = 14^? with prime divisor 7
>
> So in that construction of a solution to FLT there is a common divisor and so now we divide the equation by the common divisor, and we get this:
>
> 1^y + 1^y = 1^y
> 1^z + 2^z = 1^z
> 1^w + 1^w = 2^w
>
> And those are impossible constructions. So the proof of FLT requires Generalized FLT be proven first in order to display that a Generalized FLT proof cannot co-exist unless FLT has no solutions.
>
> Now this is the moment in 2019 where I like to make that more clear. For there are many puzzled and scratching heads of thinking on how that Generalized FLT so easily proves Regular FLT. Let me write it as clear as possible.
>
> So in Generalized FLT to prove Regular FLT we can easily do that by saying all solutions have a prime factor. Suppose a Regular FLT solution set exists, then it has a prime factor. So, multiply that prime factor --out-- yes, multiply it out, AND BECAUSE OF THAT ALGEBRA AXIOM I WAS PLAYING WITH, that multiplied out factor would also have to be a solution set-- and keep multiplying out by constant k, but then you reach a point where you have no prime factor and cannot be a solution due to Generalized FLT. It cannot be a solution because it has no prime factor, and Generalized FLT says -- All Solutions have a prime factor. Contradictory to the axiom that every multiplication by k is a solution to A^k + B^k = C^k
>
> Let me show you the above by a numbers example.
>
> 12^2 + 16^2 = 20^2 has prime factor 2 so divide out the prime factor leaves 6^2 + 8^2 = 10^2 which has another prime factor of 2 divide it out leaves 3^2 + 4^2 = 5^2 and here we no longer have a prime factor. This example shows that Axiom of Algebra, that you can always retain equality with any constant number k as (kA)^2 + (kB)^2 = (kC)^2. Try it out yourself by plugging in for k any whole number or any fraction and you preserve equality.
>
> So Generalized says that if we have a solution 12^2 + 16^2 = 20^2 we can divide out the solution by the prime factor which is 2 in our sample. But the question is-- can the equation remaining be a solution? And yes of course 6^2 + 8^2 = 10^2 but if it is a solution, it must be able to be divided out by a prime factor by Generalized. And this chain of events eventually comes down to where you can no longer have a prime factor 3^2 + 4^2 = 5^2. And Generalized demands always, every solution have a prime factor. So here we have a impossibility or as mathematicians like to call it-- a Contradiction. Thus, the idea of a Regular FLT having a solution set conflicts and contradicts what was proven by Generalized FLT. That means a Regular FLT can never have a solution set. QED
>
> Very crude dot picture of 5f6, 94TH
> ELECTRON DOT CLOUD of 231Pu
>
>
> ::\ ::|:: /::
> ::\::|::/::
> _ _
> (:Y:)
> - -
> ::/::|::\::
> ::/ ::|:: \::
>
> One of those dots is the Milky Way galaxy. And
> each dot represents another galaxy.
>
>
> . \ . . | . /.
> . . \. . .|. . /. .
> ..\....|.../...
> ::\:::|::/::
> --------------- -------------
> --------------- (Y) -------------
> --------------- --------------
> ::/:::|::\::
> ../....|...\...
> . . /. . .|. . \. .
> . / . . | . \ .
>
>
> http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
>
> I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
>
> https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
> Archimedes Plutonium
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