# Tagged Questions

The number $\pi$ is the ratio of a circle's circumference to its diameter. Understanding its various properties and computing its numerical value drove the study of much mathematics throughout history. Questions regarding this special number and its properties fit in here.

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### Show that $\pi$ is a primitive recursive number [on hold]

Can anyone provide a proof that $\pi$ is a primitive recursive number, or suggest how I might prove it? Thanks
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### Can any number sequence be found in $\pi$? [duplicate]

I read somewhere that any finite number sequence must be found in $\pi$. For example, $0998975645455$ must be somewhere in the digits of $\pi$. The reason for this was that $\pi$ is irrational, ...
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### Why would we use the radius of a circle instead of the diameter when calculating circumference?

Forgive me if this question is a little too strange or maybe even off. Mathematics has never been my strong point, but I definitely think it's the coolest... Anyway, I was looking into tau, pi's up-...
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### $e^{\left(\pi^{(e^\pi)}\right)}\;$ or $\;\pi^{\left(e^{(\pi^e)}\right)}$. Which one is greater than the other?

$\newcommand{\bigxl}[1]{\mathopen{\displaystyle#1}} \newcommand{\bigxr}[1]{\mathclose{\displaystyle#1}}$ $$\large e^{\bigxl(\pi^{(e^\pi)}\bigxr)}\quad\text{or}\quad\pi^{\bigxl(e^{(\pi^e)}\bigxr)}$$ ...
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### Proving $\pi \gt e+\frac{1}{e} \gt \pi-\frac{1}{\pi} \gt e$

I created this problem for myself as a fun exercise. I want to prove the following statement: $$\pi \gt e+\dfrac{1}{e} \gt \pi-\dfrac{1}{\pi} \gt e$$ I found that the following upper/lower bounds ...
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### Can the sum of a finite series equal $\pi$?

Can the sum of a finite series equal $\pi$? I'm assuming of course that no element in the series is some fraction of $\pi$. I'm wondering since all methods I've seen of calculating $\pi$ involve ...
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### How do we know the ratio between circumference and diameter is the same for all circles?

The number $\pi$ is defined as the ratio between the circumeference and diameter of a circle. How do we know the value $\pi$ is correct for every circle? How do we truly know the value is the same ...
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### How to find the correct value of pi? [duplicate]

Pi is defined as the ratio of $\frac{c}{r}$. Many ancient scintist try to find the value of pi. Some of the values are $\frac{22}{7}$(good hold upto 10 decimal point), $\frac{355}{113}$ (good hold ...
### Improve upon: $\sqrt[4]{3^4+2^4+\frac{1}{2+(\frac{2}{3})^2}} \approx \pi$ [closed]
So here we have an approximate value of $\pi$. $$\sqrt[4]{3^4+2^4+\frac{1}{2+(\frac{2}{3})^2}} \approx \pi$$ $$3.14159265262 \ldots \approx 3.14159265358\ldots$$ How could one get a better ...