Showing posts with label triangle triplets. Show all posts
Showing posts with label triangle triplets. Show all posts

Saturday, February 28, 2015

Triangle Triplets

   Roll three dice and imagine that the three top numbers represent ‘lengths’. Can the three lengths form a triangle? Most people, without thinking, say “yes.’ But the answer is that not all whole numbers, taken as triplets, form triangles. For example, the whole numbers 2, 3, and 6 do not form a triangle but 3, 5, and 6 do form a triangle. This is easily seen by studying the following diagram.
   This becomes an interesting programming problem. There are 216 (6 x 6 x 6) possible number triplets formed by rolling ordinary, six-sided dice. Those combinations can be checked by hand (a laborious but doable activity) but what if the dice are icosahedrons like those used in Dungeons and Dragons. That’s 8 thousand combinations!
   My Scratch project Triangle Triplets quickly computes which number triplets do form triangles for 4, 6, 8, 12, and 20-sided dice. The program also counts equilateral, scalene, and isosceles triangles for each set of three dice. Using this data one can compute the probability of the number triplets forming a triangle, an equilateral triangle, a scalene triangle, or an isosceles triangle.
   You can view and download this Scratch project by clicking on this link.
   The problem has quite a history and a copy of the mathematics underlying the problem and an annotated Scratch algorithm can be had on request by sending an email to