Complex ShapesDate: Thu, 3 Nov 94 11:23:15 EST From: Brian Sledd Subject: Math Question Dr. Math, Please describe how to come up with mathematical "descriptions" for complex shapes (torus, witches hat, etc.) using three- dimensional math. Brian Date: Thu, 3 Nov 1994 20:46:52 -0500 (EST) From: Dr. Ethan Subject: Re: Math Question Hi Brian, Essentially you can do this the same way you mathematically explain things like parabolas in the plane; you just have to use two variables to parameterize it (that is the name for a mathematical description). Do you have any means for graphing three-dimensional objects? Like Mathematica (I'm sure there are others but I don't know of any). It would make this a lot easier if I could just send you some parameterizations to try. But for starters: A Sphere of radius one is all (x,y,z) that satisfy this equation: x^2 + y^2 + z^2 = 1 A Torus is all (x,y,z) that satisfy: z^2 = r^2 -(Sqrt[x^2 + y^2] - a)^2 There are a dozen ways to parameterize these and similar objects. If you have access to a graphing program tell me and I will try to send you some parameterizations that you can use. -Doctor Ethan, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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