Euler Week

This week we've been investigating polyhedra, making them, and counting their vertices, edges and faces:

Mr Euler had a formula. And it works!

We've also been investigating latin squares and Euler squares:

 In a latin square, each row and column has one of each colour:

We continued using Word documents:

 In Euler squares, you have to deal with the colour AND the shape:

Then, to finish off the week, we looked at graphs, map-colouring annd Eulerian paths, using Joel David Hamkins' fantastic booklet. We still have a bit more to do on this. On the first pages the idea is to find the minimum number of colours to colour the "graph" so that no connected vertices are the same colour, like this:

Here's some of our work in the booklet:

3D shapes

This week we have been investigating 3D shapes.  

We have tested Euler's formula of 

Faces + Vertices - Edges = 2 

and found it worked!

The formula is written as:   F+V-E = 2

We then made some polyhedra (polyhedrons) of our own.  These are 3D shapes that have only straight edges and flat faces.

We then checked that Euler's formula worked for our polyhedra.  You'll be pleased to hear it did!