The Petersen-Morley theorem, attributed to Johannes Trolle Petersen, who later published as Johannes Hjelmslev, and to Frank Morley in papers of 1897 and 1898, is a result in three-dimensional geometry about three general skew lines in space. Given three skew lines and the three lines of shortest distance between each pair of them, and then the three lines of shortest distance between each original line and its corresponding shortest-distance line, the theorem states that a single line meets all three of those last three lines at right angles. The theorem is unrelated to the graph-theoretic Petersen's theorem on perfect matchings in cubic graphs, despite the similar name.
Facts
StatementIf a, b, c are three general skew lines in space and a', b', c' are their lines of shortest distance, and p, q, r are the lines of shortest distance for the pairs (a,a'), (b,b') and (c,c'), then a single line meets p, q, and r all at right angles. 1 Classification
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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 Petersen-Morley theorem (Wikipedia)
Proved By
Source Petersen-Morley theorem (Wikipedia)
Sources
1. Petersen-Morley theorem (Wikipedia)
IntroductionQuote, Introduction
there is a single line meeting at right angles all of p, q, and r
Petersen-Morley theorem (Wikipedia)
- In Branch: Geometry, Lead sentence
Proved By: Julius Petersen, Lead paragraph
In geometry, the Petersen-Morley theorem states that, if
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