Symmetry

There are 72 NRICH Mathematical resources connected to Symmetry
Stringy Quads
problem
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Stringy quads

Age
7 to 11
Challenge level
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This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Arclets
problem
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Arclets

Age
14 to 16
Challenge level
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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".
Colouring Triangles
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Colouring triangles

Age
5 to 7
Challenge level
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Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

A Cartesian Puzzle
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A cartesian puzzle

Age
7 to 11
Challenge level
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Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
Mean Geometrically
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Mean geometrically

Age
16 to 18
Challenge level
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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?
Coordinate Challenge
problem
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Coordinate challenge

Age
7 to 11
Challenge level
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Use the clues about the symmetrical properties of these letters to place them on the grid.
LOGOSquares
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Logosquares

Age
16 to 18
Challenge level
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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.
Reflecting Squarely
problem
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Reflecting squarely

Age
11 to 14
Challenge level
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In how many ways can you fit all three pieces together to make shapes with line symmetry?

Shady Symmetry
problem
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Shady symmetry

Age
11 to 14
Challenge level
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How many different symmetrical shapes can you make by shading triangles or squares?
Folium of Descartes
problem
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Folium of descartes

Age
16 to 18
Challenge level
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Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.