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Unread 16-03-2014, 22:54
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RyanCahoon RyanCahoon is offline
Disassembling my prior presumptions
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Re: Math Quiz: Parabola Path

Quote:
Originally Posted by faust1706 View Post
This requires an understanding of calculus 1, the normal line.
This is definitely the simpler/faster way to derive the equations, but requires a separate proof that the shortest distance between the original curve and the boundary curve can be found along the normal line of the original curve. For bonus points:

Let y(x) be the original function [ y(x) = 0.0433x2 ]
Suppose f(x) is the equation describing boundary curve that we're trying to find.
Let D(x, x0) = distance between [x, y(x)] and [x0, f(x0)]
D(x, x0) = √((x - x0)2 + (y(x) - f(x0))2)

Do the derivation as the intersection between the hyperplane where the distance between the curves is 1 [ D(x, x0) = 1 ] and the hyperplane where the distance between the curves at the solution points is minimal [ d D(x, x0) / d x0 = 0 ]
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