Resources tagged with: Euler's formula

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

Broad Topics > Decision Mathematics and Combinatorics > Euler's formula

Painting by Numbers

Age 16 to 18
Challenge Level

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

Euler's Formula

Age 16 to 18

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.

Impossible Polyhedra

Age 16 to 18

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?

Euler's Formula and Topology

Age 16 to 18

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. . . .