🔄 Shape transformation 🔁 Theme repetition

isotopy

9.9

A continuous change of a shape without cutting or joining parts

noun
/ˈaɪsəˌtoʊpi/

Specialized

: isotopía

In topology, an isotopy can show that two knots are actually the same up to deformation.

Examples

The mathematician explained how an isotopy could transform one curve into another without breaking it.
Understanding isotopy is essential for studying the properties of geometric objects in higher dimensions.
The concept of isotopy is fundamental in topology.
Different isotopies can lead to unique geometric transformations.
In topology, an isotopy can show that two knots are actually the same up to deformation.
The mathematician explained how an isotopy could transform one curve into another without breaking it.
Different isotopies can lead to unique geometric transformations.

Synonyms

homotopy

vsisotopy

Specialized

1 9.9

A way to change one shape into another by bending it without cutting or gluing

is limited to continuous changes of embeddings rather than general functions

Surface Forms

isotopy singular

isotopies plural

Morphology

isotopy = iso + topy

Formed from bound Greek combining elements (iso- + -topy) that are not productive standalone English words, so learners cannot reliably infer the meaning from the parts.

Etymology

Isotopy comes from the Greek parts iso- ('equal') and topos ('place'), so you can picture 'the same place' as a memory hook. In topology, an isotopy is a change that moves a shape into another without cutting or joining it, so the idea of keeping points in the 'same place' during the move explains the name.