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.
Stage: 4 Challenge Level:
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
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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. More information on many of our other activities
can be found here.