Petersen–Morley theorem explained

In geometry, the Petersen–Morley theorem states that, if,,are three general skew lines in space, if,, are the lines of shortest distancerespectively for the pairs, and,and if, and are the lines of shortest distance respectivelyfor the pairs, and, then thereis a single line meeting at right angles all of,,and.

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

• News: F. . Morley . Frank Morley . 1897 . Proc. London Math. Soc. . 29 . 1 . 670–673 . On a regular rectangular configuration of ten lines . 10.1112/plms/s1-29.1.670.
• News: R. J. . Lyons . R. . Frith . The Petersen–Morley Theorem I. 1934 . 10.1017/S0305004100016601 . 192–196 . 30 . 2 . Math. Proc. Camb. Philos. Soc..
• News: H. F. . Baker. H. F. Baker. Verification of the Petersen–Morley Theorem . 1935. 24–26 . 11 . 1 . Proc. London Math. Soc. . 10.1112/jlms/s1-11.1.24.