Isotopy
/aɪˈsɒtəpi/noun
In topology, a continuous deformation carrying one embedding of a space into another without tearing or self-intersection.
The Greek roots
Literally: “sameness of place”
The story of the word
Same two roots as isotope, and for the same reason: isotopes occupy the same place on the periodic table, an isotopy keeps two shapes in the same place up to smooth sliding. The chemical word was suggested to Frederick Soddy in 1913 by Margaret Todd, a Scottish physician, over dinner. Mathematicians borrowed the pattern rather than the meaning, which is why a knot that can be untied by isotopy is called the unknot.
- How it travelled
- Ancient Greek → scientific coinage → English
The same roots elsewhere
Other languages reached for exactly the same Greek pieces.
Same family
In a sentence
The two knots look different but an isotopy takes one to the other.
He spent a term proving that no isotopy connects the two embeddings.