Surface Area and the First Fundamental Form

We recall the surface area formula from elementary calculus. We show by a vector identity that this can be written in terms of the first fundamental form. This gives our first example of how the determinant of the metric tensor relates to area (or volume). We apply this formula to that of a surface of revolution to derive the formula from second semester calculus.

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Видео Surface Area and the First Fundamental Form канала Mike, the Mathematician