/sci/ - Science & Math

>>7496654
And I'm back. Here's what I've got.

I developed a fairly simple algorithm to search for Euler Bricks. Then idea works like this. Start with two primitive Pythagorean triples, which have legs given by <span class="math">(a_1, b_1)[/spoiler] and <span class="math">(a_2, b_2)[/spoiler].
Let <span class="math">l = lcm(a_1, a_2)[/spoiler].
Then we will scale our original Pythagorean triples, so that they both have a side equal to <span class="math">l[/spoiler]. That is:

<span class="math">a_1\prime = a_1 \cdot \frac{l}{a_1} = l[/spoiler]
<span class="math">b_1\prime = b_1 \cdot \frac{l}{a_1}[/spoiler]
<span class="math">a_2\prime = a_2 \cdot \frac{l}{a_2} = l[/spoiler]
<span class="math">b_2\prime = b_2 \cdot \frac{l}{a_2}[/spoiler]

Let <span class="math">a = l, b = b_1 \prime, c = b_2 \prime[/spoiler]. We know <span class="math">\sqrt{a^2 + b^2}[/spoiler] is an integer, as well as <span class="math">\sqrt{a^2 + c^2}[/spoiler], so if <span class="math">\sqrt{b^2 + c^2}[/spoiler] is an integer, then <span class="math">(a,b,c)[/spoiler] is an Euler Brick. Here is a short python script which generates Euler Bricks via this method: http://pastebin.com/qSM8ZPVs.. (cont.)