The Kid Should See This

Topology Joke

Watch more with these video collections:

“The traditional joke about topologists,” mathematical artist Henry Segerman explains, “is that they can’t tell the difference between a coffee mug and a donut.”

To a topologistβ€”someone who studies shapes by focusing on the properties that don’t change when bent, stretched, twisted, or folded, without cutting or gluingβ€”a coffee mug and a donut are the same. Both objects have one hole and are topologically equivalent because they can deform one into the other. The torus is the mug’s most basic shape.

To visualize the joke, Segerman worked with Keenan Crane to design and manufacture this series of ceramic objects that transform between the coffee mug and the donut. The 2015 piece is called Topology Joke.

The University of Waterloo introduces another visualization:

“Topology studies properties of spaces that are invariant under any continuous deformation. It is sometimes called ‘rubber-sheet geometry’ because the objects can be stretched and contracted like rubber, but cannot be broken…

“Here are some examples of typical questions in Topology: How many holes are there in an object? How can you define the holes in a torus or sphere? What is the boundary of an object? Is a space connected? Does every continuous function from the space to itself have a fixed point?”

torus or donut
Find more of Henry Segerman’s 3D-printed math illustrations, mechanisms, puzzles and art, including a 3D-printed plastic Topology Joke, at Shapeways.

Previously on TKSST: Topology, a 1961 Eames film for IBM’s Mathematica Exhibit.

Plus, previously from Segerman: Three Gears Are Possible and The engineering behind the scissor gate and β€œscissors NOT gate”.

🌈 Watch these videos next...

Vi Hart’s Hexaflexagon

Rion Nakaya

Topology, a 1961 Eames film for IBM’s Mathematica Exhibit

Rion Nakaya

Three Gears are Possible

Rion Nakaya

The Universal Pattern Popping Up in Math, Physics, and Biology

Rion Nakaya

The Sphere-Packing Problem

Rion Nakaya

The Pythagorean theorem water demo

Rion Nakaya

The mysterious isochronous curve – The Curiosity Show

Rion Nakaya

The Kresling-Pattern and our origami world

Rion Nakaya

The Hypercube: Projections and Slicing (1978), an animated tour of a 4-dimensional cube

Rion Nakaya

Thank you to this week's sponsor:
Β