Regular polygons and circles

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

problem

Favourite

Olympic rings

Age

5 to 7

Challenge level

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?

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Favourite

Logosquares

Age

16 to 18

Challenge level

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.

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Favourite

Hex

Age

11 to 14

Challenge level

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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Favourite

Approximating pi

Age

14 to 18

Challenge level

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

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Favourite

Semi-detached

Age

14 to 16

Challenge level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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Favourite

Overlapping again

Age

7 to 11

Challenge level

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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Favourite

So big

Age

16 to 18

Challenge level

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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Favourite

Orthogonal circle

Age

16 to 18

Challenge level

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

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Favourite

Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?

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Favourite

Bracelets

Age

7 to 11

Challenge level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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For younger learners

Regular polygons and circles

Olympic rings

Logosquares

Hex

Approximating pi

Semi-detached

Overlapping again

So big

Orthogonal circle

Partly circles

Bracelets