Okay, so the Riemann Sum does the same thing that an integral does, as it is essentially measuring the area under a curve! What this means for 𝛑, is that you can measure the area (well, approximate the are) of a semicircle, multiply it by 2 to get the area of a circle, and divide by r**2, to solve for an approximate value of 𝛑!

To imagine the Riemann Sum properly, think of a semicircle, with both ends touching the x axis. Now, imagine this:

This is a good visualization of integration (or more specifically, the Riemann Sum), but what is actually going on?

Well, there are two ways to explain this: The Calculus way, or the Summation way.

First off, the Calculus method is fairly concise and easy to read, but does not really help all that much:

Cool, right? (Note from after I took that photo, the integration is not approximately the area, it is exactly the area.)

Now, the Summation way (aka the Riemann Sum) makes all this so much clearer!

(In case you do not know how to read this one, it is basically saying that, as n → ∞, it sums all of the areas of all n rectangles that fit under the curve.)

Note that, when plugged into a calculator, you can say:

Please let me know if you have any further questions!!! ^ ^*

Oh, also, please pardon my poor penmanship.. T ~ T I have not written English too much lately. (Lol)

It's not that your penmanship is bad, but might I recommend having everything that is in the images also typed out below them? Maybe for people who can't load images, screen readers, or people who need to Google Translate the writings?

Also, do you ever think that this 𝛑 thing has become an obsession? Considering the amount of time dedicated and sleep lost to calculate an already (relatively) known number?

## The Riemann Sum!

Let's talk about the Riemann Sum!!

Okay, so the Riemann Sum does the same thing that an integral does, as it is essentially measuring the area under a curve! What this means for 𝛑, is that you can measure the area (well, approximate the are) of a semicircle, multiply it by 2 to get the area of a circle, and divide by r**2, to solve for an approximate value of 𝛑!

To imagine the Riemann Sum properly, think of a semicircle, with both ends touching the x axis. Now, imagine this:

This is a good visualization of integration (or more specifically, the Riemann Sum), but what is actually going on?

Well, there are two ways to explain this: The Calculus way, or the Summation way.

First off, the Calculus method is fairly concise and easy to read, but does not really help all that much:

Cool, right? (Note from after I took that photo, the integration is not approximately the area, it is exactly the area.)

Now, the Summation way (aka the Riemann Sum) makes all this so much clearer!

(In case you do not know how to read this one, it is basically saying that, as n → ∞, it sums all of the areas of all n rectangles that fit under the curve.)

Note that, when plugged into a calculator, you can say:

Please let me know if you have any further questions!!!

^ ^*

Oh, also, please pardon my poor penmanship.. T ~ T I have not written English too much lately. (Lol)

It's not that your penmanship is bad, but might I recommend having everything that is in the images also typed out below them? Maybe for people who can't load images, screen readers, or people who need to Google Translate the writings?

Also, do you ever think that this

𝛑thing has become an obsession? Considering the amount of time dedicated and sleep lost to calculate an already (relatively) known number?@JadenGarcia Ah, okay, I can do that, of course.

Oh, and about spending so much time on 𝛑.... Never say die!

@LizFoster “Die”!? As in English “die”? Like the singular form of “dice,” or relating to death?

Or the German article?

Oh, and “Die,” there, I said it.

@JadenGarcia English "die." Is that the wrong usage?! 0~0

@LizFoster Think so, I dunno English well though, so you can't take my word for it.

@LizFoster By chance, would that be a reference to the Goonies?

@Evanlicious Ah, no, it is not. What is that?

@LizFoster Just some movie from an obscure past that I never saw. They had a quote like "Never say die!" or something.

@Evanlicious Well, seeing as she is totally unaware of the reference, she must not be using "die" correctly.

@Evanlicious Oh, ha ha ha. No, I heard it somewhere (though I do not remember where...).

@JadenGarcia Oh noooooo..

@LizFoster So... what were you intending to say? You haven't been using it incorrectly all along... have you!?

@JadenGarcia T ~ T Maybe..

@LizFoster Oh no... that can't end well, I feel sorry for you.

@LizFoster So, you never

properlyanswered the question, "is this an obsession yet"? What are your end goals? A solid not infinite length PI?@JadenGarcia Well, my real end goal is probably to discover my own approximation of 𝛑.

@LizFoster That was a correct use of the word

die, "never say die" is a saying. Which basically means that you shouldn't give up on something :-]@CodingCactus Okay, good! So they were just trolling I suppose? wwwww

@LizFoster lol, maybe? :)

@CodingCactus I've never heard it used like that in my entire life.

@JadenGarcia It's just a phrase that people use sometimes, it's kinda gone out of fashion I think tho, but it still makes sense

@CodingCactus It must've gone out of fashion.

@JadenGarcia @CodingCactus now I feel old >~<

@LizFoster Aren't you?

@JadenGarcia Not really, why? (Lol)

@LizFoster Ha, I was being sarcastic, it was a joke. I doubt you'd be that old.

@JadenGarcia Okay, good T~T

I'm glad! (Lol)