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?
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
A moveable screen slides along a mirrored corridor towards a
centrally placed light source. A ray of light from that source is
directed towards a wall of the corridor, which it strikes at 45
degrees. . . .
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
The third of three articles on the History of Trigonometry.
How far should the roof overhang to shade windows from the mid-day sun?
If you were to set the X weight to 2 what do you think the angle
Three points A, B and C lie in this order on a line, and P is any
point in the plane. Use the Cosine Rule to prove the following
The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.
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?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
The second of three articles on the History of Trigonometry.
The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.
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.
You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.
Make a clinometer and use it to help you estimate the heights of