[Math Lair] Butterfly Curve

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There are many types of geometric curves that produce beautiful, intricate shapes. One of these is the butterfly curve, a type of geometric curve that was discovered by Temple Fay at the University of Southern Mississippi. The butterfly curve can be expressed relatively simply using an equation in polar coordinates:

r = esin θ − 2 cos 4θ + sin5θ12

When plotted, it produces the following graph, which bears much resemblance to a butterfly:

[butterfly curve]

Sources used (see bibliography page for titles corresponding to numbers): 57.