What is "orthoptic"

a. Relating to orthoptics, the study and treatment of muscular irregularities of the eye. n. (context geometry English) The isoptic whose given angle is a right angle.

adj. of or relating to normal binocular vision

Orthopic may refer to:

• Orthoptic (geometry), the set of points for which two tangents of a given curve meet at a right angle, a type of isoptic
• Orthoptics, the diagnosis and treatment of defective eye movement and coordination
• A form of eye exercise designed to correct vision

In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle.

Examples:

The orthoptic of

1) a parabola is its directrix (proof: s. parabola), 2) an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is the director circle x + y = a + b (s. below), 3) a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1, \, a>b,$ is the circle x + y = a − b (in case of a ≤ b there are no orthogonal tangents, s. below), 4) an astroid x + y = 1 is a quadrifolium with the polar equation

$$r=\tfrac{1}{\sqrt{2}}\cos(2\varphi), \ 0\le \varphi <2\pi,$$
(s. below).

Generalizations: 1) An isoptic is the set of points for which two tangents of a given curve meet at a fixed angle (s. below). 2) An isoptic of two plane curves is the set of points for which two tangents meet at a fixed angle. 3) Thales' theorem on a chord $\overline{P_1P_2}$ can be considered as the orthoptic of two circles which are degenerated to the two points P, P.

Remark: In medicine there exists the term orthoptic, too.