Surface z = xy

Equation: z = x * y

z = xy is linear in each variable when the other is held fixed. A 45° rotation turns it into (u² − v²)/2, a saddle.

It is the first textbook example of a mixed partial: ∂²z/∂x∂y = 1.

Related surfaces

• Saddle surfacez = x^2 - y^2
• Breathing saddlez = sin(t) * x * y / 5
• Monkey saddlez = x^3 - 3 * x * y^2