The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. [1]
The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. [1]
The curve is given by the following parametric equations: [2]
or by the following polar equation:
The sin term has been added for purely aesthetic reasons, to make the butterfly appear fuller and more pleasing to the eye. [1]
In 2006, two mathematicians using Mathematica analyzed the function, and found variants where leaves, flowers or other insects became apparent. [3]
https://books.google.com/books?id=AsYaCgAAQBAJ&dq=OSCAR+RAMIREZ+POLAR+EQUATION&pg=PA732
r = (cos 5θ)2 + sin 3θ + 0.3 for 0 ≤ θ ≤ 6π (A polar equation discovered by Oscar Ramirez, a UCLA student, in the fall of 1991.)
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In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani. It is the intersection of a sphere with a cylinder that is tangent to the sphere and passes through two poles of the sphere. Before Viviani this curve was studied by Simon de La Loubère and Gilles de Roberval.
In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
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