Henry Ernest Dudeney/Puzzles and Curious Problems/188 - Squaring the Circle

by : $188$

 * Squaring the Circle
 * The problem of squaring the circle depends on finding the ratio of the diameter to the circumference.
 * This cannot be found in numbers with exactitude,
 * but we can get near enough for all practical purposes.


 * But it is equally impossible, by Euclidean geometry, to draw a straight line equal to the circumference of a given circle.
 * You can roll a penny carefully on its edge along a straight line on a sheet of paper and get a pretty exact result,
 * ''but such a thing as a circular garden-bed cannot be so rolled.


 * Now, the line below, when straightened out
 * (it is bent for convenience in presentation),
 * is very nearly the exact length of the circumference of the accompanying circle.


 * Dudeney-Puzzles-and-Curious-Problems-188.png


 * The horizontal part of the line is half the circumference.
 * Could you have found it by a simple method, using only pencil, compasses and ruler?