Definition:Proportion/Joint

Definition

Two real variables $x$ and $y$ are jointly proportional to a third real variable $z$ if and only if the product of $x$ and $y$ is a constant multiple of $z$:

$\forall x, y \in \R: x y \propto z \iff \exists k \in \R, k \ne 0: x y = k z$

Examples

Cylinder

The volume of a right circular cylinder varies in joint proportion as the square of the radius of its base and its height.

Also see

• Results about joint proportion can be found here.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 4$: Growth, Decay and Chemical Reactions: Problem $1$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): variation: 1. (mutual variation)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): variation: 1. (mutual variation)