Symmetry

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Making Maths: Five-Point Snowflake

Follow these instructions to make a five-pointed snowflake from a square of paper.
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Topkapi Palace

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and differences in the designs?
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Maltese Cross

Age

16 to 18

Challenge level

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.
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Hidden Meaning

Age

7 to 11

Challenge level

What is the missing symbol? Can you decode this in a similar way?
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Favourite

Octa-Flower

Age

16 to 18

Challenge level

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?
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Angular Reflection

Age

11 to 14

Challenge level

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
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A Roll of Patterned Paper

Age

14 to 16

Challenge level

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
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Rose

Age

16 to 18

Challenge level

What groups of transformations map a regular pentagon to itself?
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Flower Power

Age

11 to 16

Challenge level

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.
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Favourite

Mean Geometrically

Age

16 to 18

Challenge level

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?