# Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!)

Given my first question: What is meant by the perimeter of a Sector

1. Why is the value of $\pi$ not exactly $3$? why is it $3.14$.......... or a fraction $\frac{22}{7}$?
2. Is the value of $\pi$ of $3.14$... or $\frac{22}{7}$ the same as for $3$ dimensions?
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## closed as off topic by TonyK, Amzoti, azimut, L.G., TMMMay 18 '13 at 23:28

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Voting to close. See the linked question for motivation. Also, about "Assume no math skills": this is a mathematics forum. –  TonyK May 18 '13 at 20:44
@TonyK: very cool - "Mathematics - Stack Exchange is for people studying mathematics at any level and professionals in related fields" - FAQS –  Jawad May 18 '13 at 20:45
It's like you go to a Japanese language forum, and ask a question like "Why don't the Japanese speak English instead? You certainly won't catch me speaking Japanese!" –  TonyK May 18 '13 at 20:57
@TonyK: Right. Since I am not on home ground. Thanks a million & three. Also +1 for your previous answers. –  Jawad May 18 '13 at 20:57
@TonyK: The Greeks though a circle was in some way more perfect than a sphere and therefore the movement of Heavenly Bodies in a circle rather than a sphere which is after all just a special kind of circle. Forgive me for think that 3 is more "Perfect" than 3.14..... Forgot the example about Karl Marx arguing with God or I would post it here and that would be the end of the debate. –  Jawad May 18 '13 at 21:08

## 2 Answers

I'm not exactly sure what you mean by the value of $\pi$ for 3 dimensional applications. $\pi$ is a constant value - it is always equal to $3.1415 \ldots$.

Of course formulas don't always translate the same from 2 dimensional to 3 dimensional. For example, the area of a circle is $\pi r^2$ but the volume contained within a sphere is $\frac{4\pi}{3} r^3$. You could almost say that $\pi$ in 2 dimensional geometry is analogous to $\frac{4\pi}{3}$ but then this causes fault in other places with $\pi$, such as surface area.

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it s not true that $\pi$is always a constant, the value of $pi$ depends on number of things; for example to see how $\pi$ could be equal to 42 look at this : math.stackexchange.com/questions/254620/… –  Arjang May 18 '13 at 22:35
Area of a sphere is not $\frac{4}{3}\pi r^3$. This is the volume of a ball. Area of a sphere is $4\pi r^2$. –  tomasz May 18 '13 at 23:48
You're right, I misspoke. I forgot to switch terminology between the two cases. –  Jon Claus May 19 '13 at 3:46

There are several ways to define $\pi$, but whichever you choose it is a number that happens to be irrational (it's not equal to any fraction, although some fractions are close). It does represent the ratio between a circle's circumference and diameter for any circle (but not for spheres, squares, or other shapes).

With regards to your first question, a sector is a part of a circle, like a slice of pie (the food). Its perimeter consists of a round bit on the outside, and two straight bits toward the center.

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