## epicycloids

Noun

- plural form of
*epicycloid*

- In both cases the curves are
**epicycloids**; in the first case the radii of the rolling and the fixed circles are a(2n - I) /4n and a/2n, and in the second, an/(2n+ I) and a/(2n4-I), where a is the radius of the mirror and n the number of reflections. **Epicycloids**also received attention at the hands of Edmund Halley, Sir Isaac Newton and others; spherical**epicycloids**, in which the moving circle is inclined at a constant angle to the plane of the fixed circle, were studied by the Bernoullis, Pierre Louis M.**Epicycloids**also received attention at the hands of Edmund Halley, Sir Isaac Newton and others; spherical**epicycloids**, in which the moving circle is inclined at a constant angle to the plane of the fixed circle, were studied by the Bernoullis, Pierre Louis M.**Epicycloids**are also examples of certain caustics.- The path of contact which it traces is identical with itself; and the flanks of the teeth c are internal and their faces ex ternal
**epicycloids**for wheels, and both flanks and faces are cycloids For a pitch-circle of twice the P, - / radius of the rolling or describing /, -~- circle (as it is called) the internal B ~, epicycloid is a straight line, being, / E in fact, a diameter of the pitch- circle, so that the flanks of the teeth for such a pitch-circle are planes radiating from the axis.

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