Can you prove the angle properties described by some of the circle theorems?
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
How many noughts are at the end of these giant numbers?
