# Epicycloid Sentence Examples

It may be regarded as an

**epicycloid**in which the rolling and fixed circles are equal in diameter, as the inverse of a parabola for its focus, or as the caustic produced by the reflection at a spherical surface of rays emanating from a point on the circumference.In the particular case when the radii are in the ratio of I to 3 the

**epicycloid**(curve a) will consist of three cusps external to the circle and placed at equal distances along its circumference.The

**epicycloid**shown is termed the "three-cusped**epicycloid**" or the "**epicycloid**of Cremona."Leonhard Euler (Acta Petrop. 1784) showed that the same hypocycloid can be generated by circles having radii of; (a+b) rolling on a circle of radius a; and also that the hypocycloid formed when the radius of the rolling circle is greater than that of the fixed circle is the same as the

**epicycloid**formed by the rolling of a circle whose radius is the difference of the original radii.Therefore any

**epicycloid**or hypocycloid may be represented by the equations p = A sin B+,' or p---A cos B,,G, s = A sin B11.AdvertisementFor epiand hypo-cycloids and epiand hypo-trochoids see

**Epicycloid**.The curve may be regarded as an epitrochoid (see

**Epicycloid**) in which the rolling and fixed circles have equal radii.