Devil's curve
![](http://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Devils_curve_a%3D0.8_b%3D1.svg/220px-Devils_curve_a%3D0.8_b%3D1.svg.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Devils_curve_a%3D0.0-1.0_b%3D1.svg/220px-Devils_curve_a%3D0.0-1.0_b%3D1.svg.png)
In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form
- [1]
The polar equation of this curve is of the form
- .
Devil's curves were discovered in 1750 by Gabriel Cramer, who studied them extensively.[2]
The name comes from the shape its central lemniscate takes when graphed. The shape is named after the juggling game diabolo, which was named after the Devil[3] and which involves two sticks, a string, and a spinning prop in the likeness of the lemniscate.[4]
For , the central lemniscate, often called hourglass, is horizontal. For it is vertical. If , the shape becomes a circle. The vertical hourglass intersects the y-axis at . The horizontal hourglass intersects the x-axis at .
Electric Motor Curve
A special case of the Devil's curve occurs at , where the curve is called the electric motor curve.[5] It is defined by an equation of the form
.
The name of the special case comes from the middle shape's resemblance to the coils of wire, which rotate from forces exerted by magnets surrounding it.
References
External links
- Weisstein, Eric W. "Devil's Curve". MathWorld.
- The MacTutor History of Mathematics (University of St. Andrews) – Devil's curve