Theorem of Dinostratos

${\displaystyle {\frac {|AE|}{|AB|}}={\frac {2}{\pi }}}$

The Dinostratos theorem describes a property of Hippias's quadratrix , which makes it possible to use it to square the circle . It is named after the Greek mathematician Dinostratos , who built it around 350 BC. BC and also used it to square the circle. The theorem states that the quadratrix shares the side of its associated square in proportion . ${\displaystyle 2:\pi }$

Only the form of the proof is known from Pappos (Collection, Book 4, 30–32), who ascribes the squaring of the circle with this curve to Dinostratos. According to Ivor Bulmer-Thomas, this would be one of the earliest proofs of contradiction (which Euclid used extensively) in ancient mathematics.

literature

• Thomas Little Heath : A History of Greek Mathematics. Volume 1. From Thales to Euclid . Clarendon Press 1921 (reprinted by Elibron Classics 2006), pp. 225–230 ( excerpt from Google book search)
• Horst Hischer: Classical Problems of Antiquity - Examples of “Historical Anchoring” (PDF; 539 kB). In: Blankenagel, Jürgen & Spiegel, Wolfgang (Hrsg.): Mathematikdidaktik out of enthusiasm for mathematics - Festschrift for Harald Scheid . Stuttgart / Düsseldorf / Leipzig: Klett 2000, pp. 97–118.

Individual evidence

1. ^ Article Dinostratus by Ivor Bulmer-Thomas , Dictionary of Scientific Biography , Volume 4, pp. 103-105