interactivity
Introducing NRICH TWILGO
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
problem
Air Nets
Age
7 to 18
Challenge level
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
article
Ding Dong Bell
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
problem
Triangles in the middle
Age
11 to 18
Challenge level
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.
problem
The Bridges of Konigsberg
Age
11 to 18
Challenge level
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem
Instant Insanity
Age
11 to 18
Challenge level
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
article
When the angles of a triangle don't add up to 180 degrees
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.
problem
Vector walk
Age
14 to 18
Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Vector journeys
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?
problem
3D Treasure Hunt
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?
problem
Back fitter
Age
14 to 18
Challenge level
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
problem
What's that graph?
Age
14 to 18
Challenge level
Can you work out which processes are represented by the graphs?
problem
Vanishing point
Age
14 to 18
Challenge level
How can visual patterns be used to prove sums of series?
problem
Iff
Age
14 to 18
Challenge level
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
problem
Tetra Square
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.
problem
Always Perfect
Age
14 to 18
Challenge level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
article
A Rolling Disc - Periodic Motion
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?
problem
Classic cube
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?
problem
Fitting flat shapes
Age
16 to 18
Challenge level
How efficiently can various flat shapes be fitted together?
problem
Coordinated crystals
Age
16 to 18
Challenge level
Explore the lattice and vector structure of this crystal.
problem
Classical Means
Age
16 to 18
Challenge level
Use the diagram to investigate the classical Pythagorean means.
problem
Mach Attack
Age
16 to 18
Challenge level
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
problem
Painting by Numbers
Age
16 to 18
Challenge level
How many different colours of paint would be needed to paint these
pictures by numbers?
problem
Painting by functions
Age
16 to 18
Challenge level
Use functions to create minimalist versions of works of art.
problem
Set Square
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?
problem
Wrapping Gifts
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?
problem
Polar Bearings
Age
16 to 18
Challenge level
What on earth are polar coordinates, and why would you want to use them?
problem
Stonehenge
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.
problem
Trig reps
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?
problem
Escriptions
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.
problem
Middle Man
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?
problem
Maximum Scattering
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?
problem
Maths Shop Window
Age
16 to 18
Challenge level
Make a functional window display which will both satisfy the manager and make sense to the shoppers
problem
Circles ad infinitum
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?
problem
Areas and Ratios
Age
16 to 18
Challenge level
Do you have enough information to work out the area of the shaded quadrilateral?
problem
Hyperbolic thinking
Age
16 to 18
Challenge level
Explore the properties of these two fascinating functions using trigonometry as a guide.
problem
Five circuits, seven spins
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.
problem
Cheese cutting
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?
problem
Ford Circles
Age
16 to 18
Challenge level
Can you find the link between these beautiful circle patterns and Farey Sequences?
problem
Sheep in wolf's clothing
Age
16 to 18
Challenge level
Can you work out what simple structures have been dressed up in these advanced mathematical representations?