Hjelmslev's theorem
id:
hjelmslev-s-theorem-253-4650886
title:
Hjelmslev's theorem
text:
In geometry, Hjelmslev's theorem, named after Johannes Hjelmslev, is the statement that if points P, Q, R... on a line are isometrically mapped to points P´, Q´, R´... of another line in the same plane, then the midpoints of the segments PP´, QQ´, RR´... also lie on a line. The proof is easy if one assumes the classification of plane isometries. If the given isometry is odd, in which case it is necessarily either a reflection in a line or a glide-reflection, then the statement is true of any poi
brand slug:
wiki
category slug:
encyclopedia
description:
Collinearity of midpoints of segments that map 3 point on a line isometrically to another
original url:
https://en.wikipedia.org/wiki/Hjelmslev%27s_theorem
date created:
date modified:
2020-05-17T21:29:27Z
main entity:
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image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/5/51/Hjelmslev%27s_theorem.svg","width":324,"height":243}
fields total:
13
integrity:
15