Regular polygons and circles

problem
Square bisection

Age

11 to 14

Challenge level

Weekly Problem 8 - 2008
In how many ways can a square be cut in half using a single straight line cut?
problem
Semicircle in a semicircle

Age

14 to 16

Challenge level

The diagram shows two semicircular arcs... What is the diameter of the shaded region?
problem
Two regular polygons

Age

14 to 16

Challenge level

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?
problem
Like a circle in a spiral

Age

7 to 16

Challenge level

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
problem
Spirostars

Age

16 to 18

Challenge level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
problem
2 rings

Age

5 to 7

Challenge level

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
problem
Triangular hexagons

Age

7 to 11

Challenge level

Investigate these hexagons drawn from different sized equilateral triangles.
problem
LOGO challenge 12 - concentric circles

Age

11 to 16

Challenge level

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.
problem
LOGO challenge 11 - more on circles

Age

11 to 16

Challenge level

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates this relationship.
problem
Gold yet again

Age

16 to 18

Challenge level

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."