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.
Simon and Andrei used different methods to compare the sizes of
Go to last month's problems to see more solutions.
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.