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 Julius Petersen and Frank Morley.

References

• Morley, F. (1897). "On a regular rectangular configuration of ten lines". Proc. London Math. Soc. 29 (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. Cambr. Phil. Soc. 30 (2). pp. 192–196. doi:10.1017/S0305004100016601.
• Baker, H. F. (1935). "Verification of the Petersen–Morley Theorem". Proc. London Math. Soc. 11 (1). pp. 24–26. doi:10.1112/jlms/s1-11.1.24.