evolute's Usage Examples:

When the refracting curve is a circle and the rays emanate from any point, the locus of the secondary caustic is a Cartesian oval, and the evolute of this curve is the required diacaustic.

If the second medium be more highly refractive than the first, the secondary caustic is a hyperbola having the same focus and centre as before, and the caustic is the evolute of this curve.

For a circle, when the rays emanate from any point, the secondary caustic is a limacon, and hence the primary caustic is the evolute of this curve.

F B is the evolute of this circle, and for any radius DE at an angle a and corresponding tangent EG terminated by the evolute, the perpendicular distance of G from the line AD is c(cos a+a sin a).

40), as in violet; or outwards, revolute (fig.

The evolute of this ellipse is the caustic required.

His enquiries into evolutes enabled him to prove that the evolute of a cycloid was an equal cycloid, and by utilizing this property he constructed the isochronal pendulum generally known as the cycloidal pendulum.

Secondary caustics are orthotomic curves having the reflected or refracted rays as normals, and consequently the proper caustic curve, being the envelope of the normals, is their evolute.

- Transverse section of a revolute leaf.

The intrinsic P equation is s 4a sin 4,, and the equation to the evolute is s 4a cos 1P, which proves the evolute to be a similar cycloid placed as in fig.

(12) Along the stream line xABPJ, 4) o; and along the jet surface PJ, -1 >49> - oo; and putting 4 -irs/c - I, the intrinsic quation is irs/c cot 2 nO, (13) hich for n I is the evolute of a catenary.