Monday Math: Finite Fourier

I'm hoping that systematizing things - setting Monday as "the day I post about math" - will help keep me on the ball. For the moment, I'll stick with my research on polygons, but later I'll also use this slot to talk about interesting bits of math I've encountered over the years.

Last time I talked about polygons, I described a different set of numbers that characterize a polygon, instead of the coordinates of the vertices. This time, I'm going to try to justify using those numbers, and discuss how to compute them. Under the cut, if you will....

( Entering Diagon Alley )

Spectacles

In my Dunnett reread, I'm now about halfway through Scales of Gold. I commented once before about some linguistic quibbles - in particular, a reference to "maize" in a book set in the late 15th century; this time, though, I've got a more material complaint.

In this book, much is made of Niccolo's trading in eyeglasses; he deceives his enemies with a feigned interest in an eyeglass factory in Venice, and later pleases the ruler of Timbuktu by providing him with a pair of reading glasses. In both segments, it is said that eyeglasses are expensive, primarily available to the wealthy, for showing off and for the use of their attached scholars. Again, this is in the late 15th century, and it simply is not consistent with what I know about eyeglasses from other sources.

We know roughly when eyeglasses were invented - sometime around 1285. From what I've read, the importance of this lies primarily in their use by artisans - cobblers, smiths, gadget-makers and the like - because even crude eyeglasses can correct for the presbyopia of aging eyes, allowing artisans to continue to work effectively for an extra twenty years or so. Those twenty years are more productive than the previous twenty, because the worker has already learned twenty years of tricks of the trade - his lifetime productivity has more than doubled! But Dunnett has it that eyeglasses are still toys for the rich and their hangers-on almost two hundred years later.

I think I have to conclude that Dunnett fluffed this one. Sad, because she's usually very good on historical details.