/sci/ - Science & Math

>>7496920
Also note that though the algorithm is given in terms of the lcm of <span class="math">a_1, a_2[/spoiler], there are 4 ways to potentially generate a brick using two triples. Specifically, using <span class="math">lcm(a_1, a_2)[/spoiler], <span class="math">lcm(b_1, a_2)[/spoiler], <span class="math">lcm(a_1, b_2)[/spoiler], <span class="math">lcm(b_1, b_2)[/spoiler]. The script given takes advantage of this.

The attached picture is the program's output using the settings in the pastebin. The first thing of note is that the bricks repeat. Specifically, they generated up to 3 times. This is not surprising, If <span class="math">(a,b,c)[/spoiler] is an Euler Brick, <span class="math">(a,b), (b,c), (a,c)[/spoiler] are the legs of Pythagorean triples, and have corresponding primitive triples <span class="math">(a_1,b_1), (a_2,b_2), (a_3,b_3)[/spoiler]. Then applying the algorithm to any two of these three triples should result in the original brick, and there are there are three ways to choose two out of three triples.

The next result is more subtle. There are an even number of results. I encourage you to play around with the number of bricks the program generates and see that this always seems to be the case, no matter how many it bricks it generates. I will begin to show why this is the case in the next post.