For questions about mathematical constants, that are "significantly interesting in some way".
3
votes
0answers
43 views
The Tribonacci constant and the Dragon
Let $x = \frac{\ln T}{\ln 2} = 0.879146\dots$ where $T$ is the tribonacci constant, then x solves the transcendental equation,
$$4^x(2^x-1)=(2^x+1)$$
Let $x = \frac{\ln y}{\ln 2} = 1.523627\dots$ ...
11
votes
7answers
293 views
$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? [duplicate]
If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed ...
3
votes
1answer
120 views
How to derive the Golden mean by using properties of Gamma function?
The Golden mean known as $\frac{1+\sqrt{5}}{2}$.
How could one show the Golden mean can be expressed as
$$
\frac{2\cdot 3\cdot 7\cdot 8\cdot 12\cdot 13\cdots}{1\cdot 4\cdot 6\cdot 9\cdot 11\cdot ...
6
votes
1answer
98 views
Proving that $\frac{\pi}{2}=\prod_{k=2}^{\infty}\left(1+\frac{(-1)^{\frac{p_{{k}}-1}{2}}}{p_{k}} \right )^{-1}$ an identity of Euler's.
This is another identity of Euler's relating $\pi$ to the prime numbers, available here
\begin{align*}
\dfrac{\pi}{2}=\prod_{k=2}^{\infty}\left(1+\dfrac{(-1)^{\dfrac{p_{{k}}-1}{2}}}{p_{k}} \right ...
0
votes
0answers
30 views
Mathematica will not integrate with a constant [closed]
I don't know what is wrong, Mathematica will only give me the original integral but won't evaluate it. any help?
eq1 = 0.048519*x
eq2 = -0.0134
eq3 = {sin[(n*[CapitalPi]*x)/0.586667]}
eq4 = ...
2
votes
3answers
49 views
Positive constant scalar definition
In French when we say "$k$ est une constante positive", that means $k\geq 0$. But I remarked that using the same sentence in English, "$k$ is a positive constant", means that $k>0$. Can one explain ...
7
votes
2answers
201 views
Proving that $\pi=\sum\limits_{k=0}^{\infty}(-1)^{k}\left(\frac{2^{2k+1}+(-1)^{k}}{(4k+1)2^{4k}}+ \frac{2^{2k+2}+(-1)^{k+1}}{(4k+3)2^{4k+2}}\right)$
Long time ago I've been playng with formulas for $\pi$ and found that one above in the title which can also be expressed as
\begin{align*}
...
10
votes
8answers
600 views
“How I wish I could calculate pi” analogs…
You might know the mnemonic for $\pi$ in the title or even this more elaborated one:
Sir, I bear a rhyme excelling
In mystic force, and magic spelling
Celestial sprites elucidate
All my own ...
