f69r circle

[Jorge_Stolfi]

The 16-wedge subdivision of the circle and the central floral motif stood out to me. 

Just a bit of geometry:

In theory, dividing a circle into N equal sectors with ruler and compass is possible only for certain values of N.  One can divide the whole circle once into 3 sectors (easy) or 5 sectors (harder; must look it up in Euclid).  By combining the two one can get N = 3x5 = 15.  Then one can easily divide any sector in half, even using only a ruler (if the center and circle are given).  So one can get any N that is 2^k x 3^r x 5^s, where k is any non-negative integer but r and s can be only 0 or 1.  Thus one can have 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, ...  But not 7, 9, 11, 13, 14, 17, 18, 19, 21 etc.

One cannot get 360; but one could get 120 = 2^3  x 3 x 5, and then one could divide each of those tiny sectors into 3 parts with a ruler.  It would not be exact but the error would be too small to see.

In 1796 Gauss discovered that one can also divide the circle with ruler and compass into You are not allowed to view links. Register or Login to view., 257, and 65537 sides, which allows other values of N like 34, 51, 95, etc.  But the construction for 17 already is devilishly complicated...

In practice, dividing a circle into any number of equal parts can be done fairly quickly by trial and error.  But I suppose that someone who had studied Euclid would have found this approach distasteful.

But all of this is irrelevant for the VMS, because the Scribe(s) who drew the diagrams did not bother (or know how) to divide them into equal parts.  In fact, they could not even get their circles to close properly, even though they seem to have used a compass to draw them.

And anyway some (if not all) of the circular diagrams were probably copied by the VMS Author from some prior source.  Thus any preference for 16 or other special numbers is to be attributed to that source, not necessarily to the Author.

All the best, --jorge