There are 60 NRICH Mathematical resources connected to Rotations, you may find related items under Transformations and constructions.
Broad Topics > Transformations and constructions > Rotations
This problem explores the shapes and symmetries in some national flags.
Create a pattern on the small grid. How could you extend your pattern on the larger grid?
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
Explore the effect of reflecting in two intersecting mirror lines.
Why not challenge a friend to play this transformation game?
Use the clues about the symmetrical properties of these letters to place them on the grid.
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
How many different symmetrical shapes can you make by shading triangles or squares?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.
What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?
Does changing the order of transformations always/sometimes/never produce the same transformation?
See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?
I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?
A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
Points off a rolling wheel make traces. What makes those traces have symmetry?
Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?
This article describes a practical approach to enhance the teaching and learning of coordinates.
This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over.
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?
Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.
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?
How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
A red square and a blue square overlap. Is the area of the overlap always the same?
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?
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.
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.
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?
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?
Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?
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?
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Find the shape and symmetries of the two pieces of this cut cube.
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?
This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.