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One-Point Folding

Graphing Parametric Surfaces in Octave

The graph below is supposed to illustrate a surface that is formed by taking a piece of paper cut into a circle, which is then bent by putting a pencil tip at the center and pulling up on opposite points along a diameter.  The equation for the outer rim is calculated by first starting with spherical coordinates F(phi,theta) and a path of the form s(t)=(phi(t),theta(t)) where phi is longitude and theta is latitude.  The path is theta = t and phi(t) = -p cos(2t) + pi/4, with p to be determined later.  We compose F(s(t)) and compute arc length numerically for several values of p ranging from 0 to pi/4.  The length is determined to be approximately 2*pi when p = 0.5487.


Categories : mathematical

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