ZAMBOJ Michal

Calculating on a parabola

K. G. Ch. von Staudt described simple geometric constructions of arithmetic operations in his Beiträge zur Geometrie der Lage. We discuss a special case of a parabola in particular. Elementary and derived constructions of addition and multiplication are presented synthetically and analytically, and straightforward algebraic observations are interconnected with the deeper geometric properties of a parabola. We focus on constructions of arithmetic, geometric, and harmonic mean. Von Staudt´s constructions are also discussed in relation to the Matiyasevich-Stechkin parabola and Möbius´ parabolic nomogram.