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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.

Tin Tight

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

This is a useful application of Trial and Improvement.

It is not necessary to use a lot of algebra for representation where students are not sufficiently confident with that.

A systematic record of the calculation process being repeated is however very important.

A spreadsheet that allows volume to vary is powerful but only after students have established an understanding of the calculation process being carried out by the computer on their behalf.