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Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 Challenge Level:

These tilings really caught my imagination.

They comprise some basic shapes and the work is then to identify how to move from one drawing of the shape to the next.

Perhaps it might be useful to think of a shape not as a square say but as a square plus two sides. That is:

Repeat 6 [ fd 30 rt 90]

for example.