Use your mouse to move the red and green parts of this disc. Can
you make images which show the turnings described?
Can you sort these triangles into three different families and explain how you did it?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How much do you have to turn these dials by in order to unlock the
Can you describe the journey to each of the six places on these
maps? How would you turn at each junction?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Where will the point stop after it has turned through 30 000
degrees? I took out my calculator and typed 30 000 ÷ 360. How
did this help?
Can you explain why it is impossible to construct this triangle?
A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?
The sine of an angle is equal to the cosine of its complement. Can
you explain why and does this rule extend beyond angles of 90
Two perpendicular lines lie across each other and the end points
are joined to form a quadrilateral. Eight ratios are defined, three
are given but five need to be found.
Two polygons fit together so that the exterior angle at each end of
their shared side is 81 degrees. If both shapes now have to be
regular could the angle still be 81 degrees?
Two right-angled triangles are connected together as part of a
structure. An object is dropped from the top of the green triangle
where does it pass the base of the blue triangle?
Two places are diametrically opposite each other on the same line
of latitude. Compare the distances between them travelling along
the line of latitude and travelling over the nearest pole.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Prove Pythagoras' Theorem for right-angled spherical triangles.
We had some very detailed solutions to this problem - well done!
Dante, Jack and Jemma all solved this problem. Jamie even sent in a
challenge of his own!
Now you can see why there is no chance of winning!
Simon and Andrei used different methods to compare the sizes of
Bernard Bagnall describes how to get more out of some favourite
How good are you at estimating angles?
A description of how to make the five Platonic solids out of paper.
A Sudoku with a twist.
How do we measure curvature? Find out about curvature on soccer and rugby balls and on surfaces of negative curvature like banana skins.
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.