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Three Cubes

Can you work out the dimensions of the three cubes?

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When the Angles of a Triangle Don't Add up to 180 Degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

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The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This is a nice activity to take slowly and build up understanding in each part.

It also makes a nice lead in towards maths at the next level, especially if the spreadsheet is used to improve accuracy as each fustum height becomes smaller without limit.