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Ball Packing

If a ball is rolled into the corner of a room how far is its centre from the corner?

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Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

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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.

Three Balls

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Here is a hint for this tough nut. Just think about the angle between a chord and a tangent to a circle and think about cyclic quadrilaterals.