Prepuzzle puzzle: What is a random triangle?
He reprinted a story, and linked to the source, the Winter 2004 bulletin of the North Carolina Assoc of AP Math Teachers. The kid does the work based on the teacher’s definition of a random triangle:
- choosing angle A,
- choosing angle B,
- choosing angle C,
- Step 1 includes the assumption that half of all triangles are obtuse. Part of the conclusion is buried in a shaky assumption.
- Even in obtuse triangles, two thirds of the angles are acute.
- Why should we randomly choose angle measures?
What is a random triangle? how can we generate them?
I have 3 ideas:
- Lengths. Randomly choose 3 numbers on a given interval. We will get lots of non-triangles this way. On the other hand, dividing a given number into 3 pieces may skew the results – the constraint makes the process non-random.
- Coordinates. Randomly choose 6 numbers on a given interval: (a,b), (c,d), (e,f). Perhaps we can integrate? multiple integrals?
- Angles. Three numbers from (o,2π). And plot them as points on a unit circle. Will the constraint do something funny. It feels like a relative of my mad carpenter or walking stick puzzles.
Ideas? Thoughts? I can’t believe that any is worse than what the article reported.