I just found an approximation to e, in geometry. It is 99.91%

>>8724016
Post proofs.

this is fucking dumb. go play with chicken bones you fucking numerologist.

also post proof

File: NÆSTENe.gif (4MB, 564x480px) Image search: [Google]

4MB, 564x480px

OP here, Proof:
Volume of sphere:
[math] V_1= \frac{4}{3} \pi r^3 [/math]
Volume of cube:
[math] V_2=a^3 [/math]

Right triangle so that
[math]x^2+x^2=a^2 \Leftrightarrow[/math]
[math]2x^2=a^2 [/math] (1)

We realize that
[math] \displaystyle{ \left( \frac{1}{2}a \right)^2}=x^2 \Leftrightarrow [/math]
[math]\left ( \frac{1}{2}a \right )^2+x^2=r^2\Leftrightarrow
x=\sqrt{r^2-\frac{1}{4}a^2}[/math]

We'll skip the simplification and end up, when we combine the two
[math]a= \frac{2}{\sqrt{3}}r \Leftrightarrow a^3=V_2=\frac{8 \sqrt{3}}{9}[/math]

so

[math]\frac{V_2}{V_1} [/math]
...simplification...
[math]\frac{V_2}{V_1}=\frac{3 \pi}{2 \sqrt{3}} \approx 2,721 [/math]

[math] e \approx 2,718 [/math]

>>8724140
Correction with the "We realize that":
[math] \left(\frac{1}{2}a \right)^2+x^2=r^2[/math]

>>8724140
Nice find but it is not even that close desu.

Now if you can tweak the part of
>where the radius of the sphere is the length from the center to the cube's corner
so that by picking some similarly defined radii you can get arbitrarily close to e then I'll be impressed.

>>8724140
Two calculators I have say it's 2,7207.

>>8724155

For a cube containing a sphere,
r = ½a.

For a sphere containing a cube,
r = ½a√3

Substitute into either formula.