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?
Can you explain what is happening and account for the values being
On a nine-point pegboard a band is stretched over 4 pegs in a
"figure of 8" arrangement. How many different "figure of 8"
arrangements can be made ?
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
Three squares are drawn on the sides of a triangle ABC. Their areas
are respectively 18 000, 20 000 and 26 000 square centimetres. If
the outer vertices of the squares are joined, three more. . . .
The length AM can be calculated using trigonometry in two different
ways. Create this pair of equivalent calculations for different peg
boards, notice a general result, and account for it.
The Earth is further from the Sun than Venus, but how much further?
Twice as far? Ten times?
How can you represent the curvature of a cylinder on a flat piece of paper?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different?. . . .