A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?
Photocopiers can reduce from A3 to A4 without distorting the image.
Explore the relationships between different paper sizes that make
The points P, Q, R and S are the midpoints of the edges of a convex
quadrilateral. What do you notice about the quadrilateral PQRS as
the convex quadrilateral changes?
Prove Pythagoras' Theorem using enlargements and scale factors.
L triominoes can fit together to make larger versions of
themselves. Is every size possible to make in this way?
Triangle ABC is equilateral. D, the midpoint of BC, is the centre
of the semi-circle whose radius is R which touches AB and AC, as
well as a smaller circle with radius r which also touches AB and
AC. . . .
Plex lets you specify a mapping between points and their images.
Then you can draw and see the transformed image.
Using a ruler, pencil and compasses only, it is possible to
construct a square inside any triangle so that all four vertices
touch the sides of the triangle.
Introduces the idea of a twizzle to represent number and asks how
one can use this representation to add and subtract geometrically.
How can you use twizzles to multiply and divide?
The first part of an investigation into how to represent numbers
using geometric transformations that ultimately leads us to
discover numbers not on the number line.
Arrow arithmetic, but with a twist.