# Evolute Sentence Examples

evolute
• The determination of the true relation between the length of a pendulum and the time of its oscillation; the invention of the theory of evolutes; the discovery, hence ensuing, that the cycloid is its own evolute, and is strictly isochronous; the ingenious although practically inoperative idea of correcting the "circular error" of the pendulum by applying cycloidal cheeks to clocks - were all contained in this remarkable treatise.

• 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.

• 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.

• 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.

• 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.

• The evolute of this ellipse is the caustic required.

• 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.

• 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. These curves appear to have been first discussed by Gergonne.

• 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).

• Many well-known derivative curves present themselves in this manner; thus the variable curve may be the normal (or line at right angles to the tangent) at any point of the given curve; the intersection of the consecutive normals is the centre of curvature; and we have the evolute as at once the locus of the centre of curvature and the envelope of the normal.