Plane And Solid Analytic Geometry An Elementary Textbook
Plane And Solid Analytic Geometry An Elementary Textbook
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105.
HIGHER PLANE CURVES 203 107. The epicycloid. — The path described by a point Fig. 106.
204 ANALYTIC GEOMETRY [Ch. XV, § 108 on the circumference of a circle which rolls on the out- side of a fixed circle is called an epicycloid.
Let the student show that the equations of the epi- cycloid are 'a + b s x — (a-\-b~) cos (j> — b cos y = (« + b) sin — b sin b a + b * 108. The cardioid. — An important special case of the epicycloid is the cardioid, in which a = b; but instead of Fig. 107.
obtai...ning its equation as a special case of that curve, we shall find it easier to obtain its polar equation at once from the definition.
Let 0, the original point of contact of the two circles, Ch. XV, § 110] HIGHER PLANE CURVES 205 be chosen as the polar origin, and the diameter CA con- tinued through this point as the polar axis. Let the second circle roll on the first until the line of centres CC makes an angle 0G 7 O"(= >) with its original position, and let P be the new position of the point of contact.
What to read after Plane And Solid Analytic Geometry An Elementary Textbook?
You can find similar books in the "Read Also" column, or choose other free books by Charles H Charles Hamilton Ashton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
105.
HIGHER PLANE CURVES 203 107. The epicycloid. — The path described by a point Fig. 106.
204 ANALYTIC GEOMETRY [Ch. XV, § 108 on the circumference of a circle which rolls on the out- side of a fixed circle is called an epicycloid.
Let the student show that the equations of the epi- cycloid are 'a + b s x — (a-\-b~) cos (j> — b cos y = (« + b) sin — b sin b a + b * 108. The cardioid. — An important special case of the epicycloid is the cardioid, in which a = b; but instead of Fig. 107.
obtai...ning its equation as a special case of that curve, we shall find it easier to obtain its polar equation at once from the definition.
Let 0, the original point of contact of the two circles, Ch. XV, § 110] HIGHER PLANE CURVES 205 be chosen as the polar origin, and the diameter CA con- tinued through this point as the polar axis. Let the second circle roll on the first until the line of centres CC makes an angle 0G 7 O"(= >) with its original position, and let P be the new position of the point of contact.
What to read after Plane And Solid Analytic Geometry An Elementary Textbook?
You can find similar books in the "Read Also" column, or choose other free books by Charles H Charles Hamilton Ashton to read onlineMoreLess
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