This synthwave enumeration shows the creation of 32 different hypocycloids, which are curves that are obtained by following a point that lies on circle rolling inside another circle. If the ratio of the radii of the two circles is a rational number, then the described curve will close after a certain number of rotations of the inner circle (can you figure out how many rotations in terms of the ratio?). Can you determine how many cusps the curve will have in terms of the ratio? What do you think will happen if the ratio is irrational? Have you every played with spirograph?
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This animation was inspired by a fun article from Carol Schumacher and two undergraduates from the November 2021 issue of Math Horizons (where they draw generalized hypocycloids using tangle toys instead of circles). See maa.tandfonline.com/doi/full/... for more.
#manim #hypocycloid #spirograph #circle #rollingcircles #rational #count #mathvideo #math #mtbos #animation #iteachmath #mathematics #enumeration #synthwave
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