On 2015-06-13 12:10, Warren D Smith wrote:
so in view of my impossibility theorem for integer coordinates for any affined regular pentagon, I presume that means the picture by Gosper et al of a Penrose-like raster pattern, must only be approximately 5-symmetric and approximately Penrose, and presumably the approximations have something to do with the golden ratio approximations by Fibonacci ratios.
I attempted to count pixels by hand, and the sizes of the mystic pentagrams appear to be 1,5,34... which are fibos, but I might easily be mis-counting.
You know, it was quite difficult for Penrose to invent his tiling, but the Gosper et al computer construction is invented by accident by a moron. Except we are currently too dumb to figure out why it succeeded.
Yes, those Fibonacci #s were one of the very first things the Ziegler Hunts kids discovered, right after determining the Floorless period formula pi/period = arcsin(sqrt(d e)/2). (eqn 7, p7). --rwg According to http://www.tweedledum.com/rwg/rectarith12.pdf there's no (unaffined) regular pentagon in any n dimension grid. What about affined?