Without using a calculator, computer or tables find the exact
values of cos36cos72 and also cos36 - cos72.
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.
The third of three articles on the History of Trigonometry.
The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Prove that the shaded area of the semicircle is equal to the area of the inner circle.
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?
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. . . .
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
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.
If you were to set the X weight to 2 what do you think the angle
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?
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
How far should the roof overhang to shade windows from the mid-day sun?
Re-arrange the pieces of the puzzle to form a rectangle and then to
form an equilateral triangle. Calculate the angles and lengths.
One side of a triangle is divided into segments of length a and b
by the inscribed circle, with radius r. Prove that the area is:
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.
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
What is the longest stick that can be carried horizontally along a
narrow corridor and around a right-angled bend?
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
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.