# Isoptic

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 52A10 [MSN][ZBL]

The locus of intersections of tangents to a given curve meeting at a fixed angle; when the fixed angle is a right angle, the locus is an **orthoptic**.

The isoptic of a parabola is a hyperbola; the isoptic of an epicycloid is an epitrochoid; the isoptic of a hypocycloid is a hypotrochoid; the isoptic of a sinusoidal spiral is again a sinusoidal spiral; and the isoptic of a cycloid is again a cycloid.

#### References

- J.D. Lawrence, "A catalog of special plane curves" , Dover (1972) ISBN 0-486-60288-5 Zbl 0257.50002

**How to Cite This Entry:**

Isoptic.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Isoptic&oldid=51376