P is a point inside a square ABCD such that PA= 1, PB = 2 and PC =
3. How big is angle APB ?
A metal puzzle which led to some mathematical questions.
Measure the two angles. What do you notice?
Construct this design using only compasses
What is the sum of the angles of a triangle whose sides are
circular arcs on a flat surface? What if the triangle is on the
surface of a sphere?
What angle is needed for a ball to do a circuit of the billiard
table and then pass through its original position?
Make five different quadrilaterals on a nine-point pegboard,
without using the centre peg. Work out the angles in each
quadrilateral you make. Now, what other relationships you can see?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Consider a watch face which has identical hands and identical marks
for the hours. It is opposite to a mirror. When is the time as read
direct and in the mirror exactly the same between 6 and 7?
A spiropath is a sequence of connected line segments end to end
taking different directions. The same spiropath is iterated. When
does it cycle and when does it go on indefinitely?
My train left London between 6 a.m. and 7 a.m. and arrived in Paris
between 9 a.m. and 10 a.m. At the start and end of the journey the
hands on my watch were in exactly the same positions but the. . . .
Jennifer Piggott and Charlie Gilderdale describe a free interactive
circular geoboard environment that can lead learners to pose
Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.
Explore patterns based on a rhombus. How can you enlarge the
pattern - or explode it?
Suggestions for worthwhile mathematical activity on the subject of
angle measurement for all pupils.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.