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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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Gift of Gems

Four jewellers share their stock. Can you work out the relative values of their gems?

Half a Triangle

Age 14 to 16 Challenge Level:
Triangle split 50-50 for area
Using only a pair of compasses, and an edge to draw a straight line along,
construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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NRICH is part of the family of activities in the Millennium Mathematics Project.