top-ology-blog

*Follow*

top-ology-blog

“The trick to learning math is to complain constantly.”

—
Topology professor

mathprofessorquotes

When people ask me how I can be a math major and still say I’m not good with numbers, I’m like ‘here, let me draw you a picture.’

mathed-potatoes

infinityfield

Sponsored

$

American Express®

wkn-source-code

Klein Bottle

the-mathematical-poet

“In mathematics, it’s not like your professors understand everything. It’s just at some point they get comfortable with not understanding.”

—
Algebraic topology professor

mathprofessorquotes

math textbooks are the best

thanks for the helpful commentary

alexyar

In an important field of mathematics called topology, two objects are considered to be equivalent, or “homeomorphic,” if one can be morphed into the other by simply twisting and stretching its surface; they are different if you have to cut or crease the surface of one to reshape it into the form of the other.

Consider, for example, a torus — the dougnut-shape object shown in the intro slide. If you turn it upright, widen one side and indent the top of that side, you then have a cylindrical object with a handle. Thus, a classic math joke is to say that topologists can’t tell their doughnuts from their coffee cups.

On the other hand, Moebius bands — loops with a single twist in them — are not homeomorphic with twist-free loops (cylinders), because you can’t take the twist out of a Moebius band without cutting it, flipping over one of the edges, and reattaching.

Topologists long wondered: Is a sphere homeomorphic with the inside-out version of itself? In other words, can you turn a sphere inside out? At first it seems impossible, because you aren’t allowed to poke a hole in the sphere and pull out the inside. But in fact, “sphere eversion,” as it’s called, is possible.

Incredibly, the topologist Bernard Morin, a key developer of the complex method of sphere eversion shown here, was blind.

Livescience.com

mathmajik

Wikipedia’s amusingly captioned illustrations of the hairy ball theorem.

enformat

wkn-source-code

“Who needs numbers when you can have doughnuts?”

—
Topology professor

mathprofessorquotes

**August Möbius – Scientist of the Day**

August Möbius (Moebius), a German mathematician, was born Nov. 17, 1790 (*see fourth image above for a portrait*).

lindahall

A hexahedral mesh and its dual surfaces.

fasterdonuts

mathispun

The classical homeomorphism between a coffee mug and a doughnut.

curiosamathematica

“It’s too late to topologize.”

—
Graduate student

mathprofessorquotes

"I can’t tell the difference between a coffee mug and a donut"

- Professor of Topology on homeomorphism

yapblog

M.C. Escher [Maurits Cornelis Escher]; Completion Date: 1965.

magictransistor

The Riemannian Tonnetz (“tonal grid,” shown above) is a planar array of pitches along three simplicial axes, corresponding to the three consonant intervals. Major and minor triads are represented by triangles which tile the plane of the Tonnetz. Edge-adjacent triads share two common pitches, and so the principal transformations are expressed as minimal motion of the Tonnetz. Unlike the historical theorist for which it is named, neo-Riemannian theory typically assumes enharmonic equivalence (G# = Ab), which wraps the planar graph into a torus.

wkn-source-code