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# Mathmatical Notation

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I am having a few problems understanding some of the notation in my text book. For example the following equation is used for finding the intersection between a line and a plane : N.P(t) + D = 0 What does the ''=0'' part mean? Surely this equation does not always yield zero no matter what value of t you plug into it. This =0 thing crops up a lot and i is causing me trouble (i know i probably look like a dumbass now

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If the equality were always meant to be true, it would be called an "identity". An "equation" is usually a condition that will be false for some values of the variables involved and true for others. In the context of the intersection of a line and a plane, the variable is probably a parameter of the line (t). You find the value of t for which the equation holds, and you find the intersection point substituting that value in the parametrization of the line.

[edited by - alvaro on December 5, 2002 2:11:30 PM]

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so does the =0 actually mean ''false'' and would be specific to the context in which the equation was being refered to?

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No, it should mean that if you substitute the parameters needed into the equation and it works out, then the line intersects the plane.

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Brent Gunning | My Site

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it means that when "N.P(t) + D = 0", intersection has occured. when it equals a number other than 0 then it hasn''t. The zero doesn''t mean true or false as such, it''s just what it has to
evaluate to to be true.

3 + t = 5

plug in 1 and you''ll end up with 4, which is the wrong (false)answer. put in 2 and you''ll get five, so the equation becomes "true"

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I don''t know what the mathematical notation for a boolean equivalency test is, but the "=" assign generally means that the equation asserts both sides are equal.

Put another way, the "=" sign means you have an algebra problem to solve. And if there is no solution, the equation just isn''t valid for the given situation.

In C++ notation (and Java, C# I guess), the "==" notation means do a boolean test to see if the two sides are equal. Thus,

3 + t = 5 is only meaningful when t = 2.

But,

3 + t == 5 will return true if t = 2, and false if t is anything else.

Now, for the N.P(t) + D = 0 equation, N and D are fixed (defining the plane) and P varies according to t. The equation implies that you may be able to find a value of t for which the equation is satisfied. It''s an algebra problem and you have to solve for t.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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