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Questions tagged [constants]

For questions about mathematical constants, that are "significantly interesting in some way".

A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way". Constants arise in many different areas of mathematics. Constants such as $e$ and $\pi$ occur in diverse contexts such as geometry, number theory and calculus.

What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste. Some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places.

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What are the uses of Euler's number $e$?

People make such a big deal of the number $e$. I do not get why it is so important, other than the fact that $\ln(x)=\log_e(x)$. People say it is used all over mathematics and such, but they never give me examples. Where is the number $e$ used?…
Anonymous Computer
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What is the logic behind Kaprekar's Constant?

Kaprekar's constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will…
Adit T.
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a simple formula linking the value of $e$ to the Golden Ratio $\phi$

These last days, I was looking for an approximation formula to $\pi$. But, surprisingly, the formulas led to this other one: $$ e = \left (\frac {\phi} {\phi - 1} \right)^{\frac {1} {2\text{Log}\phi}}\text{where }\phi\text { is the Golden Ratio} :…
Eddy Khemiri
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If $\pi $ is a normal number, is $\tau $ one?

If $\pi$ is a normal number, would that imply that $\tau =2\pi $ is also a normal number? If so, why? Something tells me that it should be, but I have no idea how to prove it. If all digits of $\pi$ were either $0$, $1$, $2$, $3$ or $4$, the proof…
user132181
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Is there any significance of Euler's number other than being the base for the exponential function?

It seems like most natural situations (that at least I've come across) where Euler's number shows up, there's usually a more general (yet still natural) version of it that contains the exponential function. Even its usual definition as: $$e =…
TC159
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Math constants generalization

Does any generalization for "famous" math constants (like $\pi$ or $e$) exist. I know how those constants are useful, but I do not know what property makes them useful. Is there any definition of those numbers which can include some additional…
Vasoli
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Is there a known mathematical constant for the formula $f(x)=\sum_{n=1}^\infty(\prod_{m=1}^{n}(\frac{1}{m}))$?

I'm not a mathematician nor do I otherwise use it seriously, but every once in a while I just play around with a formula that I generate (usually to look complex or designed to get really big [like a factorial function]), but this time, I think I…
Curtis Sheppard
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Does this have a name? (Regarding ways to calculate e)

Just wondering...came across this relationship regarding Euler's number in my math tinkerings, but I'm unaware if this particular relationship has a specific name or not: $$\lim_{x\to\infty}\frac{x^x}{(x-1)^{x-1}} - \frac{(x-1)^{x-1}}{(x-2)^{x-2}} =…
Steve Beresh
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Terms that cannot be solved for a variable

Yesterday our analysis professor told us you cannot solve $$ y = e^x+2/(1+x^2) $$ for x, but you have the option to approximate this numerically. He did not prove that, he just noted it. I can't believe that's true and am very unsatisfied with that.…
bot47
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Euler's method to compute the number Napier's constant

I am asking about the original way that Euler did to calculate Napier's constant, I heard that he was able to compute its first 23 decimals.
Anas Shaikhany
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calculating the position of a given digit in a constant (e.g. $\pi$)

I'm aware that there are a lot BBP type formulas out there which extract the n-th digit of the observed constant. I'm asking for the reverse action, namely, is it possible to find the first occurrence of a given digit (or string of digits) within a…
user3209815
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Mathematical constants

Am I mistaken, or is there a mistake on the mathematical constants Wikipedia page that describes the Conic constant / Schwarzschild constant in terms of Napier's constant?
martin
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can a constant in a max be taken outside

A really silly question, but can I do: $$\max_x \left( c \cdot f(x) \right) = c \cdot \max_x f(x)$$ It seems that way, since I'm just interested in the maximum value of $f(x)$ which is not influenced by a constant and it shouldn't matter if I…
agricola
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What is the value of $a + b + s + t$

I'm confused as to how to approach this. I've tried to foil it out. $$x^3(3x-1)=a+bx+sx^2+tx^3$$ The equation above is true for all values of $x$, where $a$, $b$, $s$, and $t$ are constants. What is the value of $a+b+s+t$?
Hamza
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How to prove this equality about e

I have the assumption that the following holds: $$\lim_{n \to \infty}\frac{1}{n^2} \cdot \sum_{i = 0}^n \left(1 - \frac 1n \right)^i = 1 - \frac{2}{e}.$$ However, I am totally not sure about it. How can I prove or try to prove it?
Sacha
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