next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

SINUSOID

Curve studied for the first time by Roberval in 1636, under the name "companion of the roulette". |

Cartesian equation: .
Transcendental curve. Length on a period, given by an elliptic integral of the second kind: . In the case a = b: . |

The sinusoid is the trajectory of a movement composed of a sinusoidal motion (i.e. the projection on a line of a uniform circular motion) and of a motion of uniform translation:

If the plane of the sinusoid is winded into a cylinder
of revolution with generatrix *Oy* and radius *nb*, then we get
the cylindric
sine wave: .

When *n * = 1, it is an ellipse of eccentricity ,
and therefore, the expansion of a planar section of a cylinder of revolution
is a sinusoid: concretely, the trace of the edge of a bevelled candle,
rolling on a plane, is a sinusoid:

The orthogonal projection of a circular helix on a plane parallel to its axis is a sinusoid.

See also the egg box, the revolution of the sinusoid, the sine surface.

next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

© Robert FERRÉOL 2017