Acute and Obtuse Triangle Simulation
- Taylor Gibson
It may be suprsing to learn that if you were to create triangles at random, it is significantly more likely that you will create an obtuse triangle than acute or right. This Monte Carlo simulation creates a triangle by randomally selecting the sizes of it's three angles. A running percentage is kept on how many of the triangles are acute and obtuse with the results graphed on the right. For sufficiently large trials, the graphs will approach a limiting value. Geogebra is not designed for such a simulation, so it is rather resource intensive. Your computer may skip a few trials in order to keep up with the graphs, so don't be surprised to see only 495 trials completed if you ask for 500.
Some good topics for discussions to have with your students: How can you analytically prove what is being demonstrated? Why does this simulation not concern itself with right triangles?