Compute any arbitrary digit of pi. In hexidecimal.

Yes that's the one thanks for linking to it.
I have that in one of my programs where I have to calculate the value of pi to an arbitrary number of digits.

 

The 1960s, String Theory and LSD.

 

 

 

Even cooler is the Lambert W function.

 

Even cooler is the Lambert W function.

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Yes that's a cool thing in math and can help with some electrical circuits.

It would be hard for me to name the most beautiful equation or expression in math as I see it. There are so many.
One that stands out because we use it a lot is the Laplace Transform and companion the Inverse Laplace Transform. It's amazing how we see a helix from a different angle become a sine wave or damped sine wave. That would be called a 3d projection onto a 2d surface.

There are many simpler ones too that are collectively referred to as "witches", and others called "asteroids". Both of these are really just line curves but it's amazing how they look like things we've all seen in real life even before we knew anything about math. Then we have the lemniscates which can sometimes form familiar looking shapes also.

Then we have the rotational 3d objects and the generated 2d lines/curves. Some of these are amazing too.
Of course the Fractals are at the head of the class here, it's hard to beat the beauty that can be found in these things both for the finished appearance and also the beauty of the simple math functions that create them

 

Yes that's a cool thing in math and can help with some electrical circuits.

It would be hard for me to name the most beautiful equation or expression in math as I see it. There are so many.
One that stands out because we use it a lot is the Laplace Transform and companion the Inverse Laplace Transform. It's amazing how we see a helix from a different angle become a sine wave or damped sine wave. That would be called a 3d projection onto a 2d surface.

There are many simpler ones too that are collectively referred to as "witches", and others called "asteroids". Both of these are really just line curves but it's amazing how they look like things we've all seen in real life even before we knew anything about math. Then we have the lemniscates which can sometimes form familiar looking shapes also.

Then we have the rotational 3d objects and the generated 2d lines/curves. Some of these are amazing too.
Of course the Fractals are at the head of the class here, it's hard to beat the beauty that can be found in these things both for the finished appearance and also the beauty of the simple math functions that create them

The most beautiful equation is:

\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)

Where:

\(A\) is the money accumulated after \(t\) years
\(P\) is the principal amount
\(r\) is the annual interest rate
\(n\) is the number of times the interest is compounded per year.
\(t\) is the time span in years

 

The most beautiful equation is:

\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)

Where:

\(A\) is the money accumulated after \(t\) years
\(P\) is the principal amount
\(r\) is the annual interest rate
\(n\) is the number of times the interest is compounded per year.
\(t\) is the time span in years

My man!

 

The most beautiful equation is:

\(A = P \left(1 + \frac{r}{n}\right)^{nt}\)

Where:

\(A\) is the money accumulated after \(t\) years
\(P\) is the principal amount
\(r\) is the annual interest rate
\(n\) is the number of times the interest is compounded per year.
\(t\) is the time span in years

Ha ha, yeah, I have to agree fully especially when 'A' is large ha ha

I forgot to include one of the best, although its beauty arises from a different standpoint. That's the partial differential wave equation which ties in with the speed of light:




where 'c' is the speed of light.

I guess we could also argue that the time dilation (and related) equations are beautiful in that they describe reality better than anything that came before that.
For example, now Mark Kelly has to celebrate his birthday 5 milliseconds sooner than his twin brother

 

Mandelbrot Zoom World Record, Part 1:

and it continues...11 parts, 24 hours.

I'll feature these at my next party.

 

I'll feature these at my next party

If you do that, I suggest you stick to beer ...

 

Mandelbrot Zoom World Record, Part 1:

and it continues...11 parts, 24 hours.

I'll feature these at my next party.

So that's what it looks like to fall into a Black Hole right after a really huge number of snails fell in just before you did.

 

I you do that, I suggest you stick to beer ...

You mean instead of LSD right?

 

 

I always found some originators of ideas in various areas to have a name that amazingly coincides with what they came up with.
For example, the Poynting Vector, which points in the direction of energy flow. From what I gather the name "Poynting" is actually pronounced in English as "pointing", which of course means to point in a certain direction with say the forefinger.
It's almost comical sometimes.

 

String Theorists Accidentally Find a New Formula for Pi

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As Saha and Sinha discovered more than 600 years later, Madhava’s formula is only a special case of a much more general equation for calculating pi. In their work, the string theorists discovered the following formula:

​

This formula produces an infinitely long sum. What is striking is that it depends on the factor λ , a freely selectable parameter. No matter what value λ has, the formula will always result in pi. And because there are infinitely many numbers that can correspond to λ, Saha and Sinha have found an infinite number of pi formulas.

 

String Theorists Accidentally Find a New Formula for Pi
View attachment 330453​

I am not sure of the significance of this find, but it's still interesting. I've always found that trying to find new ways to calculate pi has always been interesting. The usual idea though is to try to find as few digits as possible to get as many digits of pi as possible.
For example:
22/7 gives us 3 or 4 digits, and so we only gained maybe 1/2 digit (one function and 3 digits to get just over 3 digits of pi).
A little better is:
cuberoot(31) which gives us 4 or 5 digits, so that's one function and 2 digits to get just over 4 digits, so that's a good improvement.

The idea is to find a coincidence between the numbers and functions, that's about it, that lead to a good approximation of pi.
It might be a little interesting that we end up with these things by accident. What else could we find by accident.

 

String Theorists Accidentally Find a New Formula for Pi
View attachment 330453​

Finally something useful out of string theory.
https://forum.allaboutcircuits.com/threads/beauty.150513/post-1919852

 

This was an unexpectedly fun article:

https://bigthink.com/starts-with-a-bang/projectiles-dont-make-parabolas/

 

New math.