The Wallace-Bolyai-Gerwien Theorem answers the question of when one polygon can be cut into a finite number of pieces and reassembled, using translations and rotations, into a second polygon, showing that this is always possible exactly when the two polygons have equal area. Named for William Wallace, who proved the result in 1807, and for Farkas Bolyai and Paul Gerwien, who independently proved it again in the 1830s, it is the foundational theorem of scissors congruence for polygons in the plane.
Facts
StatementOne polygon can be cut into a finite number of pieces and recomposed by translations and rotations into another if and only if the two polygons have the same area. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
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.
In Branch
Sources
1. Wallace-Bolyai-Gerwien theorem (Wikipedia)
Introduction, sentence 3
states that this can be done if and only if two polygons have the same area
Introduction, sentence 4
Wallace had proven the same result already in 1807
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.