Rotations

There are 61 NRICH Mathematical resources connected to Rotations
Middle Man
problem

Middle Man

Age
16 to 18
Challenge level
filled star empty star empty star
Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?
Rolling Triangle
problem

Rolling Triangle

Age
11 to 14
Challenge level
filled star filled star filled star
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Weighty Problem
problem

Weighty Problem

Age
11 to 14
Challenge level
filled star empty star empty star
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.
Hand Swap
problem

Hand Swap

Age
14 to 16
Challenge level
filled star filled star empty star
My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?
Illusion
problem

Illusion

Age
11 to 16
Challenge level
filled star filled star filled star
A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?
Cubic Spin
problem

Cubic Spin

Age
16 to 18
Challenge level
filled star filled star empty star
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?
Get Cross
problem

Get Cross

Age
14 to 16
Challenge level
filled star filled star empty star
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?
Coke machine
problem

Coke machine

Age
14 to 16
Challenge level
filled star empty star empty star
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Cut Cube
problem

Cut Cube

Age
16 to 18
Challenge level
filled star filled star filled star
Find the shape and symmetries of the two pieces of this cut cube.
Star Find
problem

Star Find

Age
5 to 7
Challenge level
filled star filled star empty star
Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?