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math.GT2021
Music of moduli spaces
Robert Penner
A musical instrument, the plastic hormonica, is defined here as a birthday present for Dennis Sullivan, who pioneered and helped popularize the hyperbolic geometry underlying its c…
math.GT2021
Super Hyperbolic Law of Cosines: same formula with different content
Robert Penner
We derive the Laws of Cosines and Sines in the super hyperbolic plane using Minkowski supergeometry and find the identical formulae to the classical case, but remarkably involving…