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9. Square Pegs...

Which is a better fit in respect of the area occupied: a square peg in a round hole, or a round peg in a square hole?

Scroll down the page for the answer.

For the round peg in a square hole...

area of square = d 2

area of circle = pi d 2 / 4

area of circle / area of square = (pi d 2 / 4 ) / d 2

area of circle / area of square = pi / 4

area of circle / area of square = 78.5%

For the square peg in a round hole...

area of circle = pi r 2

now r 2 = x 2 + x 2

so r 2 = 2x 2
and x = r / sqr 2

so length of square = 2r / sqr 2

area of square = 4r 2 / 2

area of square = 2r 2

area of square / area of circle = 2r 2 / pi r 2

area of square / area of circle = 2 / pi

area of square / area of circle = 63.7%

so the round peg is a better fit...;-)

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