There are 70 NRICH Mathematical resources connected to Symmetry, you may find related items under Transformations and constructions.
Broad Topics > Transformations and constructions > Symmetry
Are these statements always true, sometimes true or never true?
Use the information on these cards to draw the shape that is being described.
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?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Can you place the blocks so that you see the reflection in the picture?
Use the clues about the symmetrical properties of these letters to place them on the grid.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
How many symmetric designs can you make on this grid? Can you find them all?
How many different symmetrical shapes can you make by shading triangles or squares?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
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?
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
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?
Can you deduce the pattern that has been used to lay out these bottle tops?
Find out about Emmy Noether, whose ideas linked physics and algebra, and whom Einstein described as a 'creative mathematical genius'.
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?
Plot the graph of x^y = y^x in the first quadrant and explain its properties.
An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?
Someone at the top of a hill sends a message in semaphore to a friend in the valley. A person in the valley behind also sees the same message. What is it?
What is the missing symbol? Can you decode this in a similar way?
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?
Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
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 red square and a blue square overlap. Is the area of the overlap always the same?
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?
An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?
The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.
Sketch the graphs for this implicitly defined family of functions.
Find the shape and symmetries of the two pieces of this cut cube.
This activity investigates how you might make squares and pentominoes from Polydron.