# ParametrizationWatch

Thread starter 10 years ago
#1
I know it sounds stupid but how can i parametrize a square?
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10 years ago
#2
for what purpose, exactly? some sort of double-integral over a region? a contour integral? painting your bedroom????

tell us what's on your mind!
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Thread starter 10 years ago
#3
Ehehe, I need it for a line integral..... (So i need the position vector r for the points of the square in some sort of parametrization)..... Thanks!!
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10 years ago
#4
Hmm, I think it would have to be a piecewise parametrisation...
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10 years ago
#5
Yes. In practical terms, it's simplest to split the integral into 4 pieces, with each piece being 1 side.
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10 years ago
#6
Well here is an example for a parameterization of a square in the plane with corners and .

given by

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10 years ago
#7
(Original post by Jake22)
Well here is an example for a parameterization of a square in the plane with corners and .

given by

But when it comes down to doing the integral, you're pretty certain to end up writing

.

In which case you might as well define

f(t) = (0, t), g(t) = (t,1), h(t)=(1,1-t), k(t) = (1-t, 0) and

The definitions are simpler, and you're more likely to be able to spot any useful symmetries in the integrals.
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10 years ago
#8
Yeah, I wasn't thinking of using it for anything, just wanted to give a quick example of a parameterization. If I were to integrate over the curve, I would just use the linear substitutions from my parameterization after splitting it into the sum of four integrals as you have outlined.
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