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January 29th, 2017, 03:59 AM   #1
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From: Saudi Arabia

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Paradoxical Geometrical Result

Hi,

In his papers trying to give a geometrical proof for Fermat Conjecture, Dr. Keia (*) gave a proof that the 2D Pythagoras theorem:
$$x^2 + y^2 = z ^2$$
generates, by some geometrical transformation, an equality of octahedrons, keeping the same 2D base, i.e. the equation :

$$\frac{\sqrt{2}}{3}x^3 + \frac{\sqrt{2}}{3}y^3 = \frac{\sqrt{2}}{3}z^3$$

Which also means $$x^3 + y^3 = z ^3$$

Which is absurd!

As this cannot be true for most of the (x,y,z) 2d-Pythagorean Integers triple.

If someone has a correction to my understanding, this would be helpful..

Thanks in advance!

(*) check Revolution in the Pythagoras theorem?| Interesting Engineering
Attached Images picture_for_post_in_forum.JPG (60.7 KB, 1 views) January 30th, 2017, 05:28 AM #2 Senior Member   Joined: Feb 2010 Posts: 711 Thanks: 147 $\displaystyle x^3+y^3=z^3$ has infinitely many solutions. Here is one: $\displaystyle x=1$, $\displaystyle y=2$, $\displaystyle z=\sqrt{9}$. However there are no solutions to this equation over the positive integers. A quick glance at his paper and also looking at his youtube video shows that he never mentions positive integers. My take? He's a crank. Tags geometrical, paradoxical, result Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post puppypower123 Algebra 2 March 27th, 2016 02:41 PM Ryan_aus Algebra 2 January 19th, 2014 05:48 AM kahalla Advanced Statistics 0 March 9th, 2010 01:24 AM grappler Algebra 1 June 11th, 2009 08:22 AM ^e^ Real Analysis 15 March 14th, 2007 10:39 AM

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