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Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Can you work out which processes are represented by the graphs?
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
How can visual patterns be used to prove sums of series?
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
How efficiently can various flat shapes be fitted together?
What on earth are polar coordinates, and why would you want to use them?
How many different colours of paint would be needed to paint these pictures by numbers?
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
Use functions to create minimalist versions of works of art.
For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
Explore the lattice and vector structure of this crystal.
Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?
Use the diagram to investigate the classical Pythagorean means.
The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?
A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
Make a functional window display which will both satisfy the manager and make sense to the shoppers
Explore the properties of these two fascinating functions using trigonometry as a guide.
Can you find the link between these beautiful circle patterns and Farey Sequences?
In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
Can you work out what simple structures have been dressed up in these advanced mathematical representations?