Mma 7.0 just startled me by turning the Fourier series for the line Pi -- (4 Pi - 3 t + I Sqrt[3] t), 0 <= t <= 2 Pi, 3 into -I t 2 LerchPhi[E , 2, -] 3 (I t)/3 I t 1 L(t):= --------------------- + E LerchPhi[E , 2, -]. (2 I t)/3 3 E But L(t + 2 Pi) = E^(2 Pi/3) L(t). I.e., translating by 2 Pi *rotates* by 120 degrees! Eh? Sure enough, plotting L(t), 0 < t < 6 Pi, draws a perfect equilateral triangle. There seems to be such a relation among n-1 Lerchs for each regular n-gon. Some simple consequence of n-secting the series? Psychoanalytic continuation. --rwg PS, Veit Elser's difference map algorithm, http://en.wikipedia.org/wiki/Difference_map_algorithm , has become only the second entity to solve the 82% Arnold Dozenegger disk packing puzzle completely unaided. (Not counting Emma Cohen, who got massive clues from Emma Cohen.) Also, it's clear that Rod Stephenson's clustering algorithm will do it, probably in ~1 hr --way longer than Veit's, who clearly has something dangerous. ------- Merriam-Webster's Unabridged: Main Entry: prince albert Usage: usually capitalized P&A Etymology: after Prince Albert Edward (later Edward VII king of England) [...] 2 : a man's house slipper with a low counter and goring on each side ALGORISMIC MICROGLIAS