Plane and solid analytic geometry; an elementary textbook (1905)
Ashton, Charles H. (Charles Hamilton), 1866- · New York, C. Scribner's Sons · leaf 220
ortant special case is the four-cusped hypo-cycloid, in which a = 4:b. The equations here reduce to X = ^a cos (f) -\- ^a cos 3 <^, ?/ = I rt sin (f) — ^ a sin 3 (/>. But sin 3^=3 sin <^ — 4 sin^ <^, cos 3 (^ = 4 cos^ (/) — 3 cos c^. Ch. XV, § 107] Hence x=^ a cos^ (^,and y = ^ «iii^… … 107. The epicycloid.—The path described by a point r >^ \ ~~~^ X^^l/ / / /V47^ A A J/ 1 X \ 0 JV M Fig. 106. 204 ANALYTIC GEOMETRY [Cii. XV, § 108 Oil the ciicuinfereiice of a circle Avliich rolls on the out-side of a fixed circle is called an epicycloid. Let the student show that the equations…
Geometry, Analytic
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