2006-16.md

course	course_year	question_number	tags	title	year
Geometry	IB	16	IB 2006 Geometry	3.I.2H	2006

Show that the Gaussian curvature $K$ at an arbitrary point $(x, y, z)$ of the hyperboloid $z=x y$, as an embedded surface in $\mathbf{R}^{3}$, is given by the formula

$$K=-1 /\left(1+x^{2}+y^{2}\right)^{2} .$$