Sine, cosine, tangent
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problemLying and Cheating
Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!
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problemDodecawhat
Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
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problemA Scale for the Solar System
The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?
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problemRound and Round
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
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problemCircle Box
It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
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problemEight Ratios
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.
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problemSix Discs
Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?