You Can't Put a Square Peg in a Round Hole!
Question 1: Which fits better - a round peg in a square hole or a square peg in a round hole? (Thinking)
Question 2: Consider pairing regular polygonal shapes, other than a square, with the round peg and round hole. (Ex: An equilateral triangular peg and hole with a round peg and hole or a regular pentagonal peg and hole with a round peg and hole). Do you always get the same results as in the original question??
Any help is much appreciated! (Rofl)
Re: You Can't Put a Square Peg in a Round Hole!
1. Find the area of the biggest circle which fits through a square, find the area of the biggest square which fits through a circle. Think about the area of the peg relative to the area of the hole.
2. What happens to the shape of a regular polynomial when the number of sides gets extremely large? How well will it fit through a circular hole?