Definition:Subnormal (Analytic Geometry)

Definition

Let $\CC$ be a plane curve embedded in a Cartesian plane.

Let $P$ be a point on $\CC$.

Let $\NN$ be the normal to $\CC$ at $P$.

Let $Q$ be the $x$-intercept of $\NN$.

Let $AP$ be the line through $P$ perpendicular to the $x$-axis meeting the $x$-axis at $A$.

The subnormal to $\CC$ at $P$ is the straight line segment $AQ$.

Thus the subnormal is the projection of the length of the normal onto the $x$-axis.

Also see

• Definition:Subtangent

• Results about subnormals in the context of analytic geometry can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): subnormal
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): tangent: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): subnormal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): tangent: 1.