# 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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### PI aproximation with the ${x\over y^2 } \approx \pi$ pattern

there are commands in mathematica and maple for finding Rational integer forms that approximate a floating point or a decimal number ... Mathematica function Rationalize Maple function ...
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### Determine which of the two numbers $e^{\pi}$ and $\pi ^e$ is greater. [duplicate]

Prove the inequality $e^x > (1 + x)$ using LMVT for all $x \in R$ and use it to determine which of the two numbers $e^{\pi}$ and $\pi ^e$ is greater. I proved the inequality. Now how do I ...
1answer
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### Algorithm for computing an approximate value of $\sqrt{\pi}$

I seek a simple algorithm or function that will produce an approximate value for $\sqrt{\pi}$, but none that begin with the actual value of $\pi$, then derive the root via approximation. This is very ...
1answer
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### Geometrical representation of square of pi?

a) Let's say I have a circle with a diameter $1$. Then a perimeter is $π$ (pi) and ratio between a perimeter and a diameter is $π$. b) I want to use π as a diameter of another circle, which gives a ...
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1answer
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### What does this infinite product come out to?

$$1\cdot \frac{1}{2}\cdot 3\cdot \frac{1}{4}\cdot 5\cdot \frac{1}{6}\cdots$$ What does this product come out to? It does diverge, but products like this tend to have values $\lt \infty$. Here is what ...
2answers
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### Find a function $f(x)$ in an integral

(Related question here). Is there a way to calculate the function $f(x)$ in this integral in terms of $x$ without using $a,b,c$: $$\int_{a}^{b} f(x)dx=c$$ Two examples $\rightarrow$ how do find ...
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1answer
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### Can we show that the decimal expansion of $\pi$ doesn't occur in the decimal expansion of the Champernowne constant?

This question was inspired by an answer and some comments to this question. Recall that the Champernowne constant is obtained by concatenating all natural numbers written in base 10 and then put ...
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### Decimal Expansion of Pi

Sorry if this has been asked before, but I have a query about the notion that the decimal expansion of pi contains every possible string of numbers (please note that I am only a "casual" maths ...
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### Number system and PI

Ok, we all use the decimal system with numbers from 0 to 9. And we have PI with an infinite number of decimals. We also have a boolean system or hexadecimal. Is there any decimal system where PI has ...