How to measure the Earth's diameter with a meter stick, a stopwatch, and some math.

As demonstrated in a PUMAS example from Lin H Chambers, "How Now, Pythagoras", master carpenters regularly make practical use of geometry and, at times, the Pythagorean theorem in their craft. I found this out some time ago when a good friend told me how an old-time carpenter he worked with calculated square roots using a carpenter's square.

The isoperimetric theorem states that: "Among all shapes with an equal area, the circle will be characterized by the smallest perimeter" which is equivalent to "Among all shapes with equal perimeter, the circle will be characterized by the largest area." The theorem's name derives from three Greek words: 'isos' meaning 'same', 'peri' meaning 'around' and 'metron' meaning 'measure'. A perimeter (= 'peri' + 'metron') is the arc length along the boundary of a closed two-dimensional region (= a planar shape).