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About: Petersen–Morley theorem     Goto   Sponge   NotDistinct   Permalink

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In geometry, the Petersen–Morley theorem states that, ifa,b,care three general skew lines in space, ifa′,b′,c′ are the lines of shortest distancerespectively for the pairs (b,c), (c,a) and (a,b),and if p, q and rare the lines of shortest distance respectivelyfor the pairs (a,a′), (b,b′) and (c,c′), then thereis a single line meeting at right angles all ofp,q,andr. The theorem is named after Johannes Hjelmslev (who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley.