Petersen–Morley theorem

In geometry, the Petersen–Morley theorem states that, if $a$ , $b$ , $c$ are three general skew lines in space, if $a'$ , $b'$ , $c'$ are the lines of shortest distance respectively for the pairs $(b,c)$ , $(c,a)$ and $(a,b)$ , and if $p$ , $q$ and $r$ are the lines of shortest distance respectively for the pairs $(a,a')$ , $(b,b')$ and $(c,c')$ , then there is a single line meeting at right angles all of $p$ , $q$ , and $r$ .

The theorem is named after Johannes Hjelmslev (who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley.

References[edit]

Morley, F. (1897). "On a regular rectangular configuration of ten lines". Proc. London Math. Soc. Vol. 29, no. 1. pp. 670–673. doi:10.1112/plms/s1-29.1.670.
Lyons, R. J.; Frith, R. (1934). "The Petersen–Morley Theorem I". Math. Proc. Camb. Philos. Soc. Vol. 30, no. 2. pp. 192–196. doi:10.1017/S0305004100016601.
Baker, H. F. (1935). "Verification of the Petersen–Morley Theorem". Proc. London Math. Soc. Vol. 11, no. 1. pp. 24–26. doi:10.1112/jlms/s1-11.1.24.