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## Limits and Oar-Building

A friend of mine who, among other things, builds boats (like the four-oared gig seen at the right), was describing to me one manner of oar-production.You start with a typical piece of lumber, long and square.  You cut down a certain amount from each of the four corners.  Now from each of the eight corners, you cut down a smaller amount.  The cross-sections look something like this:

Through practice, the builder knows how much wood to remove at each stage.  You can continue to repeat this process, but some sanding at this point will probably get you pretty close to what you are looking for, namely, a circle!

Naturally, this brings to mind the idea that as you increase the number of sides of a polygon of fixed radius, the polygon becomes more and more like a circle.  Indeed, the limit of such a process in indistinguishable from a circle.

I doubt those ancient oar-builders realized they were doing Calculus.