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muzik wrote:What is the equation of the curve present in x^y=y^x?

You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(-log(x)/x)x/log(x). (The logarithms are base e, naturally.)

Macbi wrote:

muzik wrote:What is the equation of the curve present in x^y=y^x?

You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(-log(x)/x)x/log(x). (The logarithms are base e, naturally.)

That would be y = W(-ln(x)/x)x/ln(x).

wwei23 wrote:

Macbi wrote:

muzik wrote:What is the equation of the curve present in x^y=y^x?

You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(-log(x)/x)x/log(x). (The logarithms are base e, naturally.)

That would be y = W(-ln(x)/x)x/ln(x).

Most mathematicians I know use "log" to mean base e (or base 2 in information theory or computer science). Using "log" to mean base 10 is uncool because 10 is just an arbitrary number with no mathematical significance. So I avoid using "ln" because if I did use it I'd be worried that people would think that I had deliberately avoided using "log", and that therefore I must be the uncool kind of person who thinks that "log" means base 10.

I managed to solve a rubik's cube in my left hand while simultaneously juggling two balls in my right hand. It took 2 minutes and 31 seconds. That was after about 15 tries.

Has any one else tried something like this before, or at least attempted to perform two skills/hobbies at once? Another one I recently did was fold a fairly neat paper crane in my left hand while juggling two balls in my right.

Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one)

Goldtiger997 wrote:Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one)

How about solving the Rubik's cube while juggling it?

...but ln has 2 letters while log has 3...

Gamedziner wrote:

Goldtiger997 wrote:Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one) :D

How about solving the Rubik's cube while juggling it?

There's some very recent prior art. Que Jianyu solved three 3x3 cubes while juggling them, in just over five minutes.

At the latest Gathering for Gardner I saw people solving cubes blindfolded, solving them with just their feet, and so on, but I didn't see any cube jugglers... I can juggle, and I can solve Rubik's Cubes, but I must say I'm not too tempted to try combining the two.

I've recently been getting into esolangs and I made this:
https://github.com/saka29/TPPL-Interpreter

Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial

gameoflifemaniac wrote:Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial

I don't get to see it at all, the moon will be under the horizon the entire time.

gameoflifemaniac wrote:Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial

Luckily, lunar eclipses aren't really "once in a lifetime", more "once in a few years".