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we say the surface element of x(u,v),y(u,v),z(u,v) is absolute value of the cross product

or

i don't understand why this is. i know that the absolute value of the cross product
is the area of a parallelogram formed by a,b,a+b, but i get lost after that

im guessing something happens where dudv cancels out with ∂u∂v then just leaves ∂r, but i can't really figure what it means.

anyone whos got into computer graphics can tell you triangles are the building blocks of surfaces, because any 3 points occupy the same plane. why a parallelogram then?

or

i don't understand why this is. i know that the absolute value of the cross product

im guessing something happens where dudv cancels out with ∂u∂v then just leaves ∂r, but i can't really figure what it means.

anyone whos got into computer graphics can tell you triangles are the building blocks of surfaces, because any 3 points occupy the same plane. why a parallelogram then?

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