A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .
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?
A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
This introduction to polar coordinates describes what is an effective way to specify position. This article explains how to convert between polar and cartesian coordinates and also encourages the. . . .
This task requires learners to explain and help others, asking and answering questions.
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
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.
Scientist Bryan Rickett has a vision of the future - and it is one
in which self-parking cars prowl the tarmac plains, hunting down
suitable parking spots and manoeuvring elegantly into them.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Find the vertices of a pentagon given the midpoints of its sides.
A and C are the opposite vertices of a square ABCD, and have
coordinates (a,b) and (c,d), respectively. What are the coordinates
of the vertices B and D? What is the area of the square?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?