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Joined 2026-09-21 Message
Incoming links: Euler characteristic of a cube boundary and its interior
History of Euler characteristic 2026-10-18
Leonhard Euler's Elementa doctrinae solidorum, or Elements of the doctrine of solids, appeared in 1758 in volume 4 of Novi Commentarii academiae scientiarum Petropolitanae, pp. 109–140. The repository record dates its composition to 1750. Composition and publication are distinct dates here.[ref]
The modern cell-count formula for Euler characteristic puts polyhedral counting into an arbitrary-dimensional CW complex. It also identifies what is being counted: the Euler characteristic of a cube boundary and its interior distinguishes a polyhedral surface from the filled solid using the missing three-dimensional term. The modern homology formulation explains why this alternating arithmetic persists across different decompositions.[ref]
Algebraic Topology by Allen Hatcher. Algebraic Topology by Allen Hatcher, §2.2, printed pp. 146–147, Theorem 2.44: alternating cell counts, homology ranks and independence from the CW structure