Definition:Orthogonal Curves
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This page is about orthogonal curves. For other uses, see orthogonal.
Definition
Let $C_1$ and $C_2$ be curves that intersect at a point $P$.
$C_1$ and $C_2$ are orthogonal at $P$ if and only if the tangent line to $C_1$ at $P$ is at right angles to the tangent line to $C_2$ at $P$.
Orthogonal Circles
Two circles are orthogonal if their angle of intersection is a right angle.
Also known as
Two objects that are orthogonal are often seen described as perpendicular.
However, the latter usually used where those objects are straight lines or planes.
Also see
- Results about orthogonal curves can be found here.
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 3$: Families of Curves. Orthogonal Trajectories
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): orthogonal
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): orthogonal
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): orthogonal curves