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isoptic |
main |
Let's have a curve C. Vary two tangents to the
curve in such a way that the angle between the two lines is a constant. Then the
intersections of the tangents form the isoptic of C.
The sinusoidal spiral is the curve for which the
isoptic is also a sinusoidal spiral.
Some isoptic curves are the following:
| curve | isoptic |
| cycloid | trochoid |
| epicycloid | epitrochoid |
| hypocycloid | hypotrochoid |
| parabola | hyperbola |
When the constant angle between the tangents has the value π/2,
the curve is called an orthoptic.
For the logarithmic spiral its orthoptic is equal to itself.
Some other orthoptic curves are:
| curve | orthoptic |
| astroid | quadrifolium |
| cardioid | limaçon |
| deltoid | circle |
| ellipse | |
| hyperbola | |
| parabola | directrix |
La Hire (1704) was the first to mention the curve.
Another curve with isoptic properties is the isoptic cubic.