Hippasus's Constant: A Proposal to Name √2 after the Discovery of Incommensurability

The square root of two is often called "Pythagoras's constant." The name has no ancient basis. The number itself was computed twelve centuries before the Pythagoreans: the Old Babylonian tablet YBC 7289 (c. 1800–1600 BC) gives √2 ≈ 1;24,51,10 = 1.41421296, within 6×10⁻⁷. What is Greek is not the number but the event: the discovery that the diagonal and the side of a square have no common measure. Ancient testimony attributes that discovery to the Pythagorean school, records that the school treated it as forbidden knowledge, and tells of a member who divulged it and perished at sea — a member named in part of the tradition as Hippasus of Metapontum. We review the sources, state what they do and do not support, and propose the name Hippasus's constant for √2: not because Hippasus first computed the number, which he did not, but because √2 is the canonical symbol of the discovery of irrationality, and that discovery is traditionally tied to his name and to his fate. https://theoryof.space