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September 18th, 2017, 05:57 AM   #1
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Curve vs Surface

I have a definition for curve and surface in my notebook that I don't really understand. Below are screenshots from the definitions and I would be really thankful if somebody explains them to me. Or you can explain to me what curve and surface is the way you know it. Thank you
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September 18th, 2017, 06:32 AM   #2
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A curve is a 1-dimensional object (a path) in $n$-dimensional space. It therefore has a single free parameter which defines the corresponding point in space.

A surface is a 2-dimensional object in $n$-dimensional space. It therefore has two free parameters which define the corresponding point in space, one parameter isn't sufficient.
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