Being curious

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Which has the greatest area, a circle or a square, inscribed in an isosceles right angle triangle?

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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.

Can you see how to build a harmonic triangle? Can you work out the next two rows?

If a sum invested gains 10% each year how long before it has doubled its value?

Explore the relationships between different paper sizes.