Proving things in space is a challenge. These tasks come from famous problems in geometry. They have intrigued the great mathematicians of the past and can do the same for the young mathematicians of the future. Famous problems in geometry are famous for very good reasons – they are interesting, challenging and good fun.

Acrobatic Cans Patterns in the Pie Patterns in the Pie - Beware Triangles Triangles The Four Colour Map Problem An Odd Thing About Vertices Points, Lines and the Spaces Between Derived Polygons The Apollonius Problem The Cantor Set

Bibliography: A list of the books which have served to inspire tasks within the EUMY Mathematics set.

Acknowledgements The author would like to acknowledge the invaluable assistance of her mathematical models who appear throughout these tasks:

Epsilon-pi and Smidgin Ubiquitous

We call them Epsi and Smidge!