A beautiful identity for cyclic quadrilaterals
Drag any vertex (colored dots) around the circle to explore the identity
Ptolemy's theorem (c. 150 AD): For any cyclic quadrilateral (vertices on a circle),
the product of the diagonals equals the sum of products of opposite sides.
It generalizes Pythagoras: when ABCD is a rectangle inscribed in a circle, AC·BD = AB·CD + AD·BC
reduces to the Pythagorean theorem.
Ptolemy used this to compute his famous chord table — essentially a table of sin values —
enabling him to predict planetary positions. Switching to the "Ptolemy & π" tab shows how
Ptolemy estimated π using inscribed polygons.