In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the Petersen–Morley theorem states that, if
,
,
are three general
skew lines
In three-dimensional geometry, skew lines are two Line (geometry), lines that do not Line-line intersection, intersect and are not Parallel (geometry), parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges ...
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 (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