An introduction to bond angle geometry.
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. . . .
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
A cube is made from smaller cubes, 5 by 5 by 5, then some of those
cubes are removed. Can you make the specified shapes, and what is
the most and least number of cubes required ?
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
How efficiently can you pack together disks?
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
Takes you through the systematic way in which you can begin to
solve a mixed up Cubic Net. How close will you come to a solution?
A cheap and simple toy with lots of mathematics. Can you interpret
the images that are produced? Can you predict the pattern that will
be produced using different wheels?
A game for 2 people. Take turns joining two dots, until your opponent is unable to move.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
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.
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.
Find the point whose sum of distances from the vertices (corners)
of a given triangle is a minimum.
Can you make a tetrahedron whose faces all have the same perimeter?
How efficiently can various flat shapes be fitted together?
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?
A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last 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.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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?
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?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Square It game for an adult and child. Can you come up with a way of always winning this game?
A game for 2 players
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?
Simple additions can lead to intriguing results...
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
Show that all pentagonal numbers are one third of a triangular number.
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
I found these clocks in the Arts Centre at the University of
Warwick intriguing - do they really need four clocks and what times
would be ambiguous with only two or three of them?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Two boats travel up and down a lake. Can you picture where they
will cross if you know how fast each boat is travelling?
Discover a way to sum square numbers by building cuboids from small
cubes. Can you picture how the sequence will grow?
What can you see? What do you notice? What questions can you ask?
Use the diagram to investigate the classical Pythagorean means.
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
This task depends on groups working collaboratively, discussing and
reasoning to agree a final product.