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Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von Frederik Tietz

Geometry of Projective Cycloids and Trochoids

The geometry of epi- and hypotrochoids, including -cycloids, as real plane curves has been studied for thousands of years. These curves are generated as the trace of a point attached to a circle rolling outside or inside a fixed circle. In my master's thesis, supervised by Michael Loenne, I investigated their complex projective closures, which are rational algebraic curves. The focus is set on the singularity analysis of the curves and their duals. The main tools are the curves' parametrisations, Bezout's theorem, and classical formulae in plane algebraic curve theory, such as the genus formula, and the generalised Pluecker formulae.