### What does **hairy ball theorem** mean?

# Definitions for hairy ball theorem

ha·i·ry ball the·o·rem

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **hairy ball theorem**.

### Wiktionary

hairy ball theoremnoun

A theorem stating that, given a sphere covered in fur, one cannot brush all the hairs flat without creating at least two whirls.

hairy ball theoremnoun

A theorem stating that there is no nonvanishing continuous tangent vector field on the sphere.

### Freebase

Hairy ball theorem

The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on even dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R³ to every point p on a sphere such that f is always tangent to the sphere at p, then there is at least one p such that f = 0. In other words, whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. The theorem was first stated by Henri Poincaré in the late 19th century. This is famously stated as "you can't comb a hairy ball flat without creating a cowlick", or sometimes "you can't comb the hair on a coconut". It was first proved in 1912 by Brouwer.

### Numerology

Chaldean Numerology

The numerical value of hairy ball theorem in Chaldean Numerology is:

**6**Pythagorean Numerology

The numerical value of hairy ball theorem in Pythagorean Numerology is:

**1**

## Translations for **hairy ball theorem**

### From our Multilingual Translation Dictionary

- teorema della palla pelosaItalian

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"hairy ball theorem." *Definitions.net.* STANDS4 LLC, 2023. Web. 9 Dec. 2023. <https://www.definitions.net/definition/hairy+ball+theorem>.

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