Themes · wave 1
Cut, Fold and Fit
Geometry problems you can solve with scissors, string and soap — and a few that took mathematicians fifty years.
Gems
The Moving Sofa Problem
What is the largest sofa you can carry round the corner of a narrow corridor? The answer took almost sixty years.
Fold and One Cut
Fold a sheet of paper, make one straight cut, unfold it, and out drops a star. Which shapes can a single cut make?
Squaring the Square
Can you cut a square into smaller squares that are all different sizes? It took until 1978 to find the smallest way.
Steiner Networks and Soap Films
What is the shortest road network joining four towns? Not the obvious one, and a soap film can find the answer for you.
Voronoi Diagrams
Split a map by asking one question, "which shop is nearest?", and you get a pattern that turns up from town planning to giraffe skin.
Pick's Theorem
Draw a shape on a grid of dots and find its area without measuring anything, just by counting dots.
The Sierpinski Carpet
Keep cutting holes in a square forever. Its area drops to zero, yet something is left, and it is not quite two-dimensional.
The Goat on a Rope
A goat eats all the grass it can reach. With pegs and ropes, can you make it eat a rectangle, a triangle or an arrow?
Rigid Polygons from a Construction Set
A square of bars wobbles, a triangle does not. Which extra bars lock a polygon, when every bar must be a whole number of holes?