Being resourceful

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.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

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

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

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

What is the same and what is different about these circle questions? What connections can you make?

Explore the relationships between different paper sizes.

Use the differences to find the solution to this Sudoku.

What do you get when you raise a quadratic to the power of a quadratic?