Coordinates

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Investigate the positions of points which have particular x and y coordinates. What do you notice?

Write down what you can see at the coordinates of the treasure island map. The words can be used in a special way to find the buried treasure. Can you work out where it is?

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?