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There are **4** NRICH Mathematical resources connected to **Euler's formula**, you may find related items under Decision mathematics and combinatorics.

Problem
Primary curriculum
Secondary curriculum
### Painting by Numbers

How many different colours of paint would be needed to paint these pictures by numbers?

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Euler's Formula

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Impossible Polyhedra

Is it possible to make an irregular polyhedron using only polygons of, say, six, seven and eight sides? The answer (rather surprisingly) is 'no', but how do we prove a statement like this?

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Euler's Formula and Topology

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.

Age 16 to 18