Squaring the Circle: rope method
Since the days of Pythagoras, a challenge in mathematics has been to "square the circle" (find a square with the same area as a given circle) using straight edge and compass only.
This topic interests me (of course), since it's the reason I called my math blog "SquareCirclez".
The following method is by Jonathan Crabtree (see "Squaring the Circle with Rope). It shows one way to "square the circle" and it can be a fun class exercise with rope. (This method is not "with straight edge and compasses" only, but it's still an interesting way to go about it.)
My proof (that the square we construct actually does have side length `sqrt(pi)`) uses Pythagoras' Theorem, and is different to Jonathan's (which uses similar triangles).
Things to do
This is a simple interactive. Step through the constructions and proof by clicking the "Next" button to see how to square the given circle using rope.
We start with a unit circle (radius `=1`). It has:
Circumference `C=2pir = 2pi`; and
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