Euler's formula

  • Paintbrush and different coloured watercolour paint blocks.
    problem

    Painting by Numbers

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

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

  • Impossible Polyhedra
    article

    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?
  • Euler's Formula
    article

    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.
  • Euler's Formula and Topology
    article

    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.

Displaying 1 - 4 of 4