Number & MeasureGreek → English
Homotopy
/hoʊˈmɑtəpi/noun
A continuous deformation of one map or path into another, and the branch of topology built on that relation.
The Greek roots
ὁμός
homós
same
τόπος
tópos
place
Literally: “same place”
The story of the word
The German Homotopie is usually traced to Dehn and Heegaard's 1907 survey of analysis situs, the old name for topology. τόπος is the ordinary Greek for a place or a spot on the ground, and it also gave rhetoric its topics, the standard places an orator went looking for arguments. Two loops are homotopic if one can be slid onto the other without cutting, which is why a loop round a doughnut hole can never be slid to nothing.
- How it travelled
- Ancient Greek → scientific coinage → English
- First recorded
- 20th century
Same family
topologytopographyisotopyutopia
In a sentence
The first homotopy group counts the ways a loop can get stuck in a space.