Adrakhonic Theorem

Definition

The Adrakhonic Theorem states that for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. In teaching it is treated as an archetypal statement about ideal geometric objects and relations, traditionally attributed to Adrakhones (early theoric figure).

Context and Usage

• Within the maths it is a standard exercise taught widely and a common point of departure for proofs and constructions. The theorem exemplifies how avout (members of the maths) reason about non-spatiotemporal, ideal forms in the Hylaean Theoric World (realm of ideal forms).
• During overland travel by a small group of avout, an icosahedral vessel was observed aloft bearing a large mosaic-like diagram that was almost certainly a proof of the Adrakhonic Theorem. Those present recognized it immediately and took it as a deliberate attempt to bypass language by appealing to shared geometry. Some described the choice as unsettling precisely because it presumed common ground.
• In a later discussion, Erasmas reports to Orolo that the Geometers (alien visitors) emblazoned the Adrakhonic Theorem on their ship; he refers to seeing a geometric proof, letters, and four planets on the hull. Orolo notes he had not viewed these before he left and had not reviewed his last image.

Related Terms

• Adrakhones — early theoric figure to whom the theorem is attributed in tradition.
• Hylaean Theoric World — the realm of ideal objects; the theorem is taught as an instance of reasoning about such forms.
• Avout — members of the maths who study and teach this result routinely.

Notes

• In running text it may appear with or without the definite article (e.g., “the Adrakhonic Theorem”); the canonical form used here omits the article.
• Accounts identifying the diagram on the icosahedral craft as a proof are presented by observers as a strong inference rather than formal certification; the emblematic intent is widely interpreted but not officially confirmed.