Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Abstract

The study of planar PH curves brings us to an unexpected acquaintance with Count Ehrenfried Walther von Tschirnhaus1 (Fig. 18.1) — a less-prominent contemporary of Huygens, Leibniz, and Newton. Born on April 10, 1651 in Kieslingswalde (now Sławnikowice in Poland), he was schooled privately and at Görlitz Gymnasium before entering the University of Leiden in 1668, where he studied philosophy, mathematics, and medicine. After completing his studies in Leiden, he travelled to England carrying a letter of recommendation from the philosopher Baruch Spinoza to Henry Oldenburg, Secretary of the newly-formed Royal Society of London for the Improvement of Natural Knowledge (and also editor of its Philosophical Transactions).