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Cut Cube

Age 16 to 18
Challenge Level Yellow starYellow starYellow star
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This problem is all about visualisation and symmetry; it might take a while to get to grips with the visualisation, and coordinates could be useful.

 

What happens when you rotate the cube about an axis through opposite vertices?

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Mean Geometrically

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?

Logosquares

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.

Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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