Fear of crowds, eating, kissing/love, rabies, words
Discuss here a little about Pythagoras, the Pythagoreans, their code of silence, punishable by death.
For the investigation you pass out lots of squares — 1×1, 2×2, 3×3, on up to 15×15 — and have them build triangles out of the sides. They write down the areas of the three squares and whether the triangle formed is obtuse, acute, or right. The conclusions follow pretty quickly from there.