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Let $S$ be a surface of revolution in $\mathbb{R}^3$ (2-dimensional) and let $C$ be its generating curve. Let $s$ be its arc lenght. Let $x = x(s)$ be the distance from a point in the curve to the $Oz$ axis (C lies in the $xz$ plane and we rotate it around $Oz$).

In my DG book, it says that

$Area(S) = 2x \int_0^l \pi(s) ds $. Where $l$ is the lenght of the curve. Although it says nowhere what this $\pi$ function is.

I've been able to prove, using the theory formulated in the book that

$Area(S) = 2\pi \int_0^l x(s) ds $ where this $\pi$ is the regular 3.14... $\pi$

The proof looks pretty correct to me. Is it safe to assume that the book was printed wrong?

thanks in advance.

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    Yes, $\pi$ here denotes the usual constant that is the ratio of any circle's circumference to its diameter (http://en.wikipedia.org/wiki/Pi). In general, if $\pi$ denotes something else (eg a coordinate projection), the notation will be made explicit.2011-10-26
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    So it was probably a typo..?2011-10-26
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    What was a typo?2011-10-26
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    Why would $pi$ be written as $pi(s)$?2011-10-26
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    that's my question, the book says there this pi(s) function. I believe it was a typo. Area(S)= 2x ∫ π(s)ds. x should be exchanged with π.2011-10-26
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    Yes it was probably a typo. If you're unsure, ask your teacher, or check if there is a list of errata for the book.2011-10-26
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    Too bad we never found out what book it was...2012-05-13
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    "Differential Geometry of curves and surfaces" by Do Carmo This one2012-06-14

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