We created this animation to visualize a fascinating set of parametric equations that produce a wide range of geometric shapes, depending on the value of the variable 𝑘. As k changes, the resulting paths trace out stars, loops, spirals, and more complex patterns. These curves are often related to epicycloids and hypocycloids, which describe the motion of a point attached to a circle rolling around another circle. When k is an integer, you get sharp, symmetric star-like shapes. Non-integer value
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