848

submitted 5 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

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[-] zkfcfbzr@lemmy.world 153 points 5 months ago* (last edited 5 months ago)

Kind of intentionally obtuse since they used eₑ as a variable and eₑₑ as another variable, and used (e-e) as an exponent a few times, which is basically the equivalent of multiplying by 1 in a fancy way. The first and last term also perfectly cancel out.

The same integral written in a saner form is:

integral from -e^e to e^e of (integral from -e^e to e^e of e^-(x^2+y^2)dy)dx

[-] xthexder@l.sw0.com 71 points 5 months ago

Wait... that's not an approximation at all! That equals exactly pi. If I understand the math correctly, it's effectively a formula for the area of a unit circle.

[-] OrganicMustard@lemmy.world 65 points 5 months ago

That should be an approximation. To get exactly pi the range of both integrals should be from minus infinity to infinity like this. It's the integral of the 2D Gaussian, which is fairly known.

[-] cryoistalline@lemmy.ml 31 points 5 months ago

The approximation is only around 4.2810^-101 off from pi.
https://www.wolframalpha.com/input?i=integral+from+-a+to+a+of+%28integral+from+-a+to+a+of+e%5E-%28x%5E2%2By%5E2%29dy%29dx
https://www.wolframalpha.com/input?i=%281-erf%28e%5Ee%29%5E2%29pi

[-] kata1yst@sh.itjust.works 41 points 5 months ago

And because it always bears repeating;

According to JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman-

Let's go to the largest size there is: the known universe. The radius of the universe is about 46 billion light years. Now let me ask (and answer!) a different question: How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, the simplest atom? It turns out that 37 decimal places (38 digits, including the number 3 to the left of the decimal point) would be quite sufficient.

[-] jlh@lemmy.jlh.name 14 points 5 months ago* (last edited 5 months ago)

Technically you need another 20 digits if you want to get down to a Planck length. (57 digits in total)

[-] daqu@feddit.org 7 points 5 months ago

So the number 3 should be close enough for home use. Good to know. Thanks!

[-] UnrepententProcrastinator@lemmy.ca 4 points 5 months ago

As an engineer, I approve this message!

[-] ulterno@lemmy.kde.social 0 points 5 months ago

My maths exam asked me to consider pi=5.

[-] vonxylofon@lemmy.world 1 points 5 months ago

"I will... consider it."

[-] bleistift2@sopuli.xyz 1 points 5 months ago* (last edited 5 months ago)

You can quote with the “greater than” sign (>). Backticks mark text as source code.

> quote

[-] xthexder@l.sw0.com 19 points 5 months ago* (last edited 5 months ago)

Ah, you're right. I was thrown off by WolframAlpha saying the integral = π ≈ 3.1416 Both of those should be ≈

(x^2 + y^2)=1 is the equation for a unit circle, so it's definitely related. Just not quite how I thought.

[-] OrganicMustard@lemmy.world 9 points 5 months ago

Also the 2D gaussian integral is used to give an insight on why the 1D gaussian integral is sqrt of pi. Here is a video with cool visualization for anyone interested.

[-] WolfLink@sh.itjust.works 5 points 5 months ago

“Fix” it with Lim as eee-> infinity (where eee is some other e-named variable)

[-] zqwzzle@lemmy.ca 72 points 5 months ago

When did dolphins learn calculus?

[-] samus12345@lemmy.world 31 points 5 months ago

[-] TSG_Asmodeus@lemmy.world 21 points 5 months ago

This is a fantastic metaphor for what tinnitus feels like.

[-] sorghum@sh.itjust.works 17 points 5 months ago

[-] Bishma@discuss.tchncs.de 13 points 5 months ago

For some reason in my head, "eeeeeeeeeeeee de eee de e" is the sounds a toddler makes when you take them to a play ground and they just start to run in wide arcs - unable to decide which piece of equipment to play on first.

So, of course, the integral of "eeeeeeeeeeeee de eee de e" would be the sound of them sleeping the car on the way home.

[-] OsrsNeedsF2P@lemmy.ml 7 points 5 months ago

Is nobody going to complain this is a screenshot of a Tumblr post of a Reddit post

[-] Dippy@beehaw.org 7 points 5 months ago

I love it but I do not understand

[-] Skua@kbin.earth 27 points 5 months ago

"e", or Euler's number, is a constant used in maths because it has useful properties in logarithms and some other things. Basically just like pi except for logarithms instead of circles. Like pi, it's an infinitely long series of non-repeating digits. The crime you have witnessed in the post is a shitload of mathematical operations applying e to e in various ways in order to get (very close to) pi. Like saying "I'm going to make 14 using only 2" and then saying (2^2^2)-2, except instead of 2 and 14 you've got e and pi

[-] Sotuanduso@lemm.ee 7 points 5 months ago

Formatting messed up (on my client at least.) It's 2^2^2, but it looks like (2^2)2 (without the parentheses, of course.)

[-] Skua@kbin.earth 3 points 5 months ago

That was the intention, yes. Thanks

[-] mogoh@lemmy.ml 2 points 5 months ago

So it is not really approximating pi and there is no circle hiding?

[-] Skua@kbin.earth 2 points 5 months ago* (last edited 5 months ago)

It's approximating the value of the actual number pi, 3.14159 etc. It's not doing anything with pi after that

[-] lugal@sopuli.xyz 7 points 5 months ago

Donno if it's part of the joke but there is a beautiful equation:

e^iπ^+1=0

So once you allow yourself to use i and log and stuff, you get a nice and simple equation

[-] fossphi@lemm.ee 2 points 5 months ago

They're also doing some shenanigans with the variable of integration. I bet it would look a lot more palatable if they were changed

[-] Kowowow@lemmy.ca 7 points 5 months ago

But what does it sound like as musical notes?

[-] Skua@kbin.earth 15 points 5 months ago* (last edited 5 months ago)

How I chose to interpret it

How it sounds

Edit: fixed a mistake and added dynamics based on the size of each E

[-] OsaErisXero@kbin.run 5 points 5 months ago

That is actually really nice sounding

[-] zzx@lemmy.world 3 points 5 months ago

Wow nice work

[-] WhiskyTangoFoxtrot@lemmy.world 3 points 5 months ago

Pretty monotonous. It's just E.

[-] Natanael@slrpnk.net 2 points 5 months ago

I'm imagining fax sounds

[-] AVincentInSpace@pawb.social 1 points 5 months ago

https://youtu.be/Qskm9MTz2V4

[-] halvar@lemm.ee 7 points 5 months ago* (last edited 5 months ago)

You may just have made me create pattern screamer and I don't exactly think it's happy at you.

[-] fionnafire 5 points 5 months ago

Alan Becker should've used this

[-] dogsoahC@lemm.ee 3 points 5 months ago

Not an equation though.

[-] KillerTofu@lemmy.world 5 points 5 months ago

What is it?

[-] WhiskyTangoFoxtrot@lemmy.world 1 points 5 months ago

I've never seen one before - no one has - but I believe it's a white hole.

[-] 0ops@lemm.ee 4 points 5 months ago

But it equals 3.14159265359

[-] IrritableOcelot@beehaw.org 1 points 4 months ago

Look, I tried to solve this with Wolfram alpha, desmos, and nunerical integration in Python, but what does a subscript e even mean?? None of the methods I tried even returned a solution, which is kinda unsurprising...how do you integrate with respect to e, when e isnt a variable??