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