The Japanese Theorem for Cyclic Polygons states that when a polygon inscribed in a circle is divided into triangles by drawing diagonals from a fixed set of vertices, the sum of the inradii of the resulting triangles is the same no matter which triangulation is chosen. It takes its name from its origin in Japanese temple geometry, the sangaku tradition of geometric problems inscribed on wooden tablets, and is a classical result illustrating an invariant hidden within an otherwise arbitrary choice of triangulation. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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StatementThe Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Japanese theorem for cyclic polygons (Wikipedia)
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1. Japanese theorem for cyclic polygons (Wikipedia)
Lead section
The Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.
In Branch: Geometry, Lead sentence
In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is
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