Your Solutions - Stage 4 & 5

Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Surprising Equalities

Age 14 to 18 Challenge Level:

Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

Quad in Quad

Age 14 to 16 Challenge Level:

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Pentagon Construction

Age 16 to 18 Challenge Level:

Follow the instructions to create a regular pentagon. Can you prove it is indeed regular?

Mixing More Paints

Age 14 to 16 Challenge Level:

Can you find an efficent way to mix paints in any ratio?

Vanishing Point

Age 14 to 18 Challenge Level:

How can visual patterns be used to prove sums of series?