Roberval found that the area under this curve is equal to three pi times its height squared, and Wren solved Pascal's challenge to determine its arc length to be eight times its height.
Roberval found that the area under this curve is equal to three pi times its height squared, and Wren solved Pascal's challenge to determine its arc length to be eight times its height. This shape is equal to both its evolute and involute, and a parametric equation for this curve is given by x equals a times quantity t minus sine of t and y equals quantity one minus cosine of t. This curve has the property that a particle along it experiences simple harmonic motion with amplitude independent of starting location, and this curve is the unique solution to the problem asking for which curve will a bead slide to another point in the least time. For 10 points, name this solution to the brachristochrome problem, the path traced out by a point on the surface of a circle rolling along a straight line.
Roberval found that the area under this curve is equal to three pi times its height squared, and Wren solved Pascal's challenge to determine its arc length to be eight times its height.
{cycloid} [prompt on “{trochoid}”]