Square Pegs in Round Holes
As the kids are taking down their tent they strike up a philosophical conversation about square pegs in round holes and thence round pegs in square holes. They ask their parents the following question:
Which fits better: a square peg in a round hole or a round peg in a square hole?
Can you help the parents solve this problem? Consider a square inscribed within a circle and circle inscribed within a square as illustrated below. In each case, find the area of the shaded section as a percentage of the whole.
Entry to this puzzle is now closed. Congratulations to the following for some great answers:
- Niall and Jenny
- Ali Raad
- Veera
- Krishi
- Sarisha
- Evgeny Mirkes
- Nora Howie
- Georges Sabback
- Patrick Luo
- Austin and Knobloch families
- Emily Lies, Jan Ricken and Tobias Beyer
- Soham Sud
- Sittichoke Som-am
- Lindsay Woodhead
- Meg North
- Ben Katz
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