Hjelmslev's theorem

Named after Johannes Hjelmslev.

Hjelmslev's theorem

1. (geometry) a theorem stating that if a set of points ${\displaystyle {P_{i}}}$ lying on a line is isometrically mapped to points ${\displaystyle {P_{i}'}}$ on a different line, then the midpoints of the segments ${\displaystyle P_{i}P_{i}'}$ also lie on a line.