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

• 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.