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# Visualising - Advanced

### Vector Journeys

### Proofs with Pictures

### Vector Walk

### Tetra Square

### What's That Graph?Live

### When the Angles of a Triangle Don't Add up to 180 Degrees

### 3D Treasure Hunt

### Vanishing Point

### Mach Attack

### Set Square

### A Rolling Disc - Periodic Motion

### Wrapping Gifts

### Fitting Flat Shapes

### Polar Bearings

### Painting by Numbers

### Stonehenge

### Painting by Functions

### Escriptions

### Coordinated Crystals

### Trig Reps

### Middle Man

### Classical Means

### Classic Cube

### Circles Ad Infinitum

### Maximum Scattering

### Maths Shop Window

### Hyperbolic Thinking

### Five Circuits, Seven Spins

### Ford Circles

### Cheese Cutting

### Sheep in Wolf's Clothing

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Age 14 to 18

Challenge Level

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?

Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Age 14 to 18

Challenge Level

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Age 14 to 18

Challenge Level

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.

Age 14 to 18

Challenge Level

Can you work out which processes are represented by the graphs?

Age 14 to 18

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.

Age 14 to 18

Challenge Level

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Age 14 to 18

Challenge Level

How can visual patterns be used to prove sums of series?

Age 16 to 18

Challenge Level

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

Age 16 to 18

Challenge Level

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?

Age 16 to 18

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?

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

How efficiently can various flat shapes be fitted together?

Age 16 to 18

Challenge Level

What on earth are polar coordinates, and why would you want to use them?

Age 16 to 18

Challenge Level

How many different colours of paint would be needed to paint these pictures by numbers?

Age 16 to 18

Challenge Level

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Age 16 to 18

Challenge Level

Use functions to create minimalist versions of works of art.

Age 16 to 18

Challenge Level

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

Age 16 to 18

Challenge Level

Explore the lattice and vector structure of this crystal.

Age 16 to 18

Challenge Level

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

Use the diagram to investigate the classical Pythagorean means.

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

Age 16 to 18

Challenge Level

Make a functional window display which will both satisfy the manager and make sense to the shoppers

Age 16 to 18

Challenge Level

Explore the properties of these two fascinating functions using trigonometry as a guide.

Age 16 to 18

Challenge Level

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

Age 16 to 18

Challenge Level

Can you find the link between these beautiful circle patterns and Farey Sequences?

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

Can you work out what simple structures have been dressed up in these advanced mathematical representations?