Pythagoras' theorem

problem

Babylon Numbers

Age

11 to 18

Challenge level

Can you make a hypothesis to explain these ancient numbers?
problem

Star Gazing

Age

14 to 16

Challenge level

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
problem

Out of the Window

Age

14 to 16

Challenge level

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
problem

Equilateral Areas

Age

14 to 16

Challenge level

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
problem

Circle Packing

Age

14 to 16

Challenge level

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
problem

Grid Lockout

Age

14 to 16

Challenge level

What remainders do you get when square numbers are divided by 4?
problem

Rhombus in Rectangle

Age

14 to 16

Challenge level

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
problem

Matter of Scale

Age

14 to 16

Challenge level

Can you prove Pythagoras' Theorem using enlargements and scale factors?
problem

Corridors

Age

14 to 16

Challenge level

A 10×10×10 cube is made from 27 2×2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
problem

Six Discs

Age

14 to 16

Challenge level

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?