Tautochrone Curve: a cycloid curve, when specifically oriented as shown, becomes a tautochrone path which has the special property that the time it takes for an object to slide to the bottom under gravity is the same no matter how high it starts up the curve. Also, the time it takes is always equal to pi times the square root of the cycloid radius divided by g. Presented here are three instances of two spheres being released at the same time, and each time they reach the bottom and collide at th

Creating a compound with #geometry #epicycloid #curve #geomet... #gears. | Beau Janzen

90K views · 1.1K reactions | Calculating the area under a cycloid curve - and why should we care in the least bit about this ~ #math #mathhack #maths #mathhelp #problemsolving #calculation #matheducation #geometry #mathematics #pi #cycloid #geometryart | Beau Janzen | Facebook

A curtate epicycloid is a fascinating type of curve generated by a point fixed at a distance less than the radius of a small circle as it rolls without slipping along the outside of a larger fixed circle. Unlike the standard epicycloid—where the tracing point lies exactly on the circumference—the curtate version creates loops that do not reach out as far, forming rounded, petal-like lobes that remain closer to the larger circle. This curve appears in various applications, including gear design a