The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful.

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# Category: Geometry

## Who (else) cares about topology? Stolen necklaces and Borsuk-Ulam by 3Blue1Brown

## A Proof That Some Spaces Can’t Be Cut by Kevin Hartnett, Quanta magazine

### Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.

### A Proof That Some Spaces Can’t Be Cut

### by Kevin Hartnett

## The maths behind ‘impossible’ never-repeating patterns by Priya Subramanian

## There are only 15 possible pentagonal tiles, research proves – from phys.org

## Equally sharing a cake between three people – with Hannah Fry on Numberphile

## The Banach–Tarski Paradox by Vsauce

## Roger Penrose explains the mathematics of the Penrose Paving – Mathematical Institute, Oxford University

The Borsuk-Ulam theorem from topology solving a counting puzzle. Truly unexpected, truly beautiful.

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