Regular polygons and circles

There are 118 NRICH Mathematical resources connected to Regular polygons and circles
Olympic rings
problem
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Olympic rings

Age
5 to 7
Challenge level
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Can you design your own version of the Olympic rings, using interlocking squares instead of circles?

Orthogonal Circle
problem
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Orthogonal circle

Age
16 to 18
Challenge level
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Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.
Partly Circles
problem
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Partly circles

Age
14 to 16
Challenge level
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What is the same and what is different about these circle questions? What connections can you make?
Bracelets
problem
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Bracelets

Age
7 to 11
Challenge level
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Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Egyptian Rope
problem
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Egyptian rope

Age
7 to 11
Challenge level
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The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Curvy areas
problem
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Curvy areas

Age
14 to 16
Challenge level
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Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Sweets in a box
problem
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Sweets in a box

Age
7 to 11
Challenge level
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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Quadarc
problem
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Quadarc

Age
14 to 16
Challenge level
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Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
Shapes on the Playground
problem
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Shapes on the playground

Age
7 to 11
Challenge level
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Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
Rolling Around
problem
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Rolling around

Age
11 to 14
Challenge level
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A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?