Abstract
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.