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Cycloid is the Brachistochrone

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Phil Todd

@polymnia

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The inverted cycloid is defined by rolling a circle below a horizontal line and tracing the locus of a point on its circumference.

You can see the definition by animating theta.

You can make the cycloid pass through point B by changing its radius.

Now press the Play button to watch the ball roll along the cycloid.  Compare its speed with a ball rolling down a straight line between A and B.

Tags: brachistochrone, cycloid, locus
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