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regular smooth curve - Penn Math

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Problem 5. A circular disk of radius 1 in the xy-plane<br />

rolls without slipping along the x-axis. The figure<br />

described by a point of the circumference of the disk<br />

is called a cycloid.<br />

(a) Find a parametrized <strong>curve</strong> �: R � R 2 whose<br />

image is the cycloid.<br />

(b) Find the arc length of the cycloid corresponding to<br />

a complete rotation of the disk.<br />

9

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