2001-10.md

course	course_year	question_number	tags	title	year
Geometry	IB	10	IB 2001 Geometry	3.I.4B	2001

State and prove the Gauss-Bonnet theorem for the area of a spherical triangle.

Suppose $\mathbf{D}$ is a regular dodecahedron, with centre the origin. Explain how each face of $\mathbf{D}$ gives rise to a spherical pentagon on the 2 -sphere $S^{2}$. For each such spherical pentagon, calculate its angles and area.