# Euler

How does water, or indeed any fluid, move? The Euler equations let us look beneath the surface and mark the beginning of modern fluid dynamics.

There are a million things in maths named after Leonard Euler. Here's a beautiful formula involving complex numbers.

In this article we explores one of Leonhard Euler's most famous results.

After 2000 years of searching we only know of 51 perfect numbers and they're all even. What else do and don't we know about these rare and precious jewels of maths?

Perfect numbers have foxed mathematicians for over 2000 years. Here's a quick look at the long struggle to find them.

Here's a quick introduction to the beauty queen amongst mathematical formulas.

One of our favourite problems from our sister site NRICH opens a door to the world of combinatorics and symmetry.

This problem about an infinite sum has a surprising answer.

This surprising result about 3D shapes tells us something deep about the nature of space.

Euler may not have cracked this problem completely, but it led to a lot of important work, including on what we today know as sudoku.

Can you move a knight on a chessboard so that it visits every square exactly once? Euler was one of the first to analyse this problem systematically, but some questions about it are still open today.

Can you find a path through on this city map that crosses every bridge exactly once? Euler's answer to this problem started off the filed of graph theory.

• Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.