Untangling the mysteries of rubbery deformations

The metric properties of modelling-clay objects change when they are deformed. Other properties, known as topological properties, remain unchanged. Surprisingly, algebra enters the picture. This naturally leads us to consider knots and the constituent molecules of DNA.

Written by

Fabien AOUSTIN

PublishedNovember 21, 2018UpdatedMay 16, 20261 min read

Untangling the mysteries of rubbery deformations

Etymologically, geometry is associated with measurement. But is the study of the objects around us really limited to a metric approach?

Does an elastic object not also retain certain properties when it is deformed? Mathematicians have answered all these questions by developing one of the richest branches of mathematics: topology.

Mathematical games with modelling clay ---------------------------

Who did not play with modelling clay as a child? Is it not fun to transform a terrifying dinosaur into an innocent little rabbit? Mathematicians enjoy playing too, though they like to add a few constraints.

This raises the following question: given two modelling-clay sculptures, is it possible to transform one continuously into the other?

Discussion

Comments

Join the discussion

No comments yet. Be the first to respond.

On the same theme

Articles recommended for you.

Math for everyone

Poincaré conjecture in manifold topology | Tangente

By the end of the 19th century, following the work of Poincaré and many other mathematicians, including Bernhard Riemann (1826–1866) and Enrico Betti (1823–1892), the topology of surfaces in our ordinary space was well understood.

Daniel LignonAug 26, 2021

Games and Challenges

Classifying knots: topology and invariants | Tangente

Knots can be combined to form new ones—or, conversely, simplified. We can borrow the vocabulary of number theory and classify them rather like the chemical elements. What varied and unexpected facets knot theory has!

ELISABETH BUSSERApr 21, 2023

History and Culture

The story of a geometry unlike any other

A science that is hard to define in a few words, topology has found its way into geometry, analysis and even algebra. How did it emerge in the mathematical world? Where is it useful? And above all, what is topology? Let's look back at the birth of a new way of seeing our space…

BERTRAND HAUCHECORNENov 21, 2018

Math for everyone

Polyhedra: from Euler's formula to Poincaré's characterization

What is a polyhedron? Throughout history, several characterizations have been proposed, only to be repeatedly undermined by the appearance of "monsters" serving as counterexamples. We look back at this epic story, which reaches its conclusion in Poincaré's work.

Jean-Jacques DupasAug 26, 2021