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2020 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.


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