Geometry Geometry Math Forum

 May 27th, 2014, 03:01 PM #1 Member   Joined: Oct 2012 Posts: 56 Thanks: 0 cube You know the integer triangles? I used those to form a cube. $\displaystyle (2mn)^2+(m^2-n^2)^2+(((m^2+n^2)^2-1)/2)^2=(((m^2+n^2)^2+1)/2)^2$ Think of a 3 4 5 triangle combined with a 5 12 13 triangle, using the hypotenuse of the first triangle to generate the second triangle. Remove the 5 and the 13. So a 3w x 4l x 12h cube has a 13 distance $\displaystyle 3^2+4^2+12^2=13^2$ When done with consecutive pell numbers the product is a perfect square. Kind of a nice coincidence which ends up being the volume. $\displaystyle 3*4*12=12^2$ 20 21 29, 29 420 421 $\displaystyle 20*21*420=420^2$ Last edited by tejolson; May 27th, 2014 at 03:35 PM. May 27th, 2014, 08:49 PM #2 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 So your question is...? May 27th, 2014, 10:23 PM #3 Senior Member   Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry It is not a cube. And it is more like an algebra problem. $\displaystyle a^2 + b^2 + c^2 = d^2$ Has infinitely many solutions. Assume, $\displaystyle a^2 + b^2 = u^2$ and $\displaystyle u^2 + c^2 = d^2$ $\displaystyle a,b,c,d,u \in \mathbb{N}$ Tags cube 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 tejolson Algebra 0 November 4th, 2013 11:13 PM Niko Bellic Algebra 6 March 6th, 2013 07:18 PM rayan Kalak Algebra 1 December 28th, 2010 05:58 AM yano Algebra 8 March 25th, 2010 06:40 PM yano Applied Math 4 December 31st, 1969 04:00 PM

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