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geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the Petersen–Morley theorem states that, if , , are three general
skew lines In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron. Two lines that both lie in the s ...
in space, if , , are the lines of shortest distance respectively for the pairs , and , and if , and are the lines of shortest distance respectively for the pairs , and , then there is a single line meeting at right angles all of , , and . The theorem is named after
Johannes Hjelmslev Johannes Trolle Hjelmslev (; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for map ...
(who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley.


References

* * * {{DEFAULTSORT:Petersen-Morley theorem Mathematical theorems Theorems in geometry