Year 9 Interactive Maths - Second Edition

Projects

Project 1.1  Euler's Formula

This project is concerned with an example of topological invariant, i.e. something that remains constant for particular shapes.

1.  For the cube shown, find:
a.  the number of vertices, v
b.  the number of edges, e
c.  the number of faces, f.

2.  Show that v – e + f = 2 for the cube.

3.  Let the corner of the cube be cut, as shown.
a.  What is the number of vertices, v?
b.  What is the number of edges, e?
c.  What is the number of faces, f?
d.  Does the result v – e + f = 2 still hold?

4.  Let the cube be sliced as shown.
a.  What is the number of vertices, v?
b.  What is the number of edges, e?
c.  What is the number of faces, f?
d.  Does the result v – e + f = 2 still hold?

5.  Let a square hole be made right through a cube, as shown.
a.  What is the number of vertices, v?
b.  What is the number of edges, e?
c.  What is the number of faces, f?
d.  Does the result v – e + f = 2 still hold?