DeepCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.2 Plane Motion: Projectiles and Cycloids, #37 · Multivariable Calculus · Curves in space

For a cardioid the radius … of the fixed circle equals the…

For a cardioid the radius $C - 1$ of the fixed circle equals the radius $1$ of the circle rolling outside (epicycloid with $C = 2$ ).
(a) The coordinates of $P$ are $x = - 1 + 2 cos θ - cos 2 θ$ , $y =_____$ . (b) The double-angle formulas yield $x = 2 cos θ (1 - cos θ)$ , $y =_____$ . (c) $x^{2} + y^{2} =_____$ so its square root is $r =_____$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.2 Plane Motion: Projectiles and Cycloids, #37

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For a **cardioid** the radius … of the fixed circle equals the…

For a cardioid the radius … of the fixed circle equals the…