ITT I learn you about some math: Gabriel's Horn

Turkey · November 13, 2014, 10:57:58 PM

First step, graph 1/x. Unless you're literally a toddler, you should know what this looks like, even you hippy poli-sci mofos:

Goddamn beautiful. But negatives are stupid so let's pretend that only numbers on the x axis exist from 1 to infinity.

Now here's where you strap on your big-boy pocket protector. Take that 2D graph, and spin that shit around the x axis. Here's what you get:

Welcome to calculus 3, integrals in three dimensions.

Why am I showing you this? This object, called Gabriel's Horn because of the Bible or some shit, has a couple interesting properties. First of all, it has infinite surface area. This might not sound so surprising because it goes on to the right for infinity. Cool, so if you have an object with literally infinite surface area, meaning it has a shell that goes on infinitely, then how much stuff can you put in it? Probably infinite volume, right? Or damn-near close (because limits or derivatives or something you heard in high school once)?

Fuck no, this shape actually has a volume of exactly pi. Infinite area on the outside, finite volume on the inside. But why is the volume equal to pi?

This shape is, essentially, an infinite set of 2D circles stacked on each other, and the area of each circle is pi*r^2 (this is like 4th grade, try to keep up). I already gave you the radius: it's 1/x. Just look at the first graph for like 10 seconds and it'll click.

So in Calculus, you can find a way to find the volume of all those circles: it's the sum of the area of each 2D circle, until infinity.

So we know the area of any of the circles is:

π*r^2 = π*(1/x)^2 = π/(x^2)

Anyone that's heard of limits can see where this is going. Take the integral of this function from 1 to infinity and you get pi. Why? Because of limits, dumbass.

What's the limit of 1/x (or 1/x^2) as x reaches infinity? It's zero. One divided by a really huge number is basically 0. So when the effect of the radius becomes insignificant, all we have left is π. /math

Turkey, out.

g💚jira · November 13, 2014, 11:05:48 PM

Quote

What's the limit of 1/x (or 1/x^2) as x reaches zero? It's zero. One divided by a really huge number is basically 0.

heheheheeh

Turkey · November 13, 2014, 11:09:44 PM

Quote from: GodspeedGojira! on November 13, 2014, 11:05:48 PM

Quote
What's the limit of 1/x (or 1/x^2) as x reaches zero? It's zero. One divided by a really huge number is basically 0.

heheheheeh

Dammit Goji.

(Thanks)

rC · November 14, 2014, 12:41:25 AM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 13, 2014, 10:57:58 PM

Welcome to calculus 3, integrals in three dimensions.

nigga Iearned how to do this in calc 1.

Spoiler

i feel smart as fuck for already knowing about everything here tho

Spoiler

(except the name of the shape)

Assassin 11D7 · November 14, 2014, 12:47:41 AM

Pi isn't a finite volume. You're maths wrong.

Idi Amin · November 14, 2014, 12:48:06 AM

Never got to third dimensional stuff in Calc. Interesting read though.

Turkey · November 14, 2014, 01:27:22 AM

Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM

Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.

Assassin 11D7 · November 14, 2014, 01:33:27 AM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM

Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.

Then what's the final decimal of Pi?

Mat Cauthon · November 14, 2014, 03:19:44 AM

>Maths
Nope

[Initialise Brain Hard Reset]

Turkey · November 14, 2014, 07:28:07 AM

Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Like I said, an irrational number is still constant. There's no such thing as an 'infinite number'.

Statefarm · November 14, 2014, 07:33:24 AM

Math

Math
Math. Math
Math math
Math

I have no idea what is going on in this thread but now I want pie

The Lord Slide Rule · November 14, 2014, 08:01:43 AM

Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM

Pi isn't a finite volume. You're maths wrong.

nigga is you dumd?

g💚jira · November 14, 2014, 08:11:18 AM

Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?

Sandtrap · November 14, 2014, 08:40:21 AM

This is beyond me.

The Lord Slide Rule · November 14, 2014, 09:39:12 AM

Thank you based Leibniz and Newton.

More Than Mortal · November 14, 2014, 10:10:18 AM

Wrong.

My stomach has infinite surface area and can contain exactly 4.865 apple pis.

The Lord Slide Rule · November 14, 2014, 10:34:21 AM

Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM

Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?

This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

g💚jira · November 14, 2014, 10:40:15 AM

Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM

Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular

The Lord Slide Rule · November 14, 2014, 10:43:44 AM

Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM

Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular

Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.

Flee · November 14, 2014, 10:56:07 AM

This user has been blacklisted from posting on the forums. Until the blacklist is lifted, all posts made by this user have been hidden and require a Sep7agon^® SecondClass Premium Membership to view.

PIXLEsauce · November 14, 2014, 11:00:19 AM

Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM

Pi isn't a finite volume. You're maths wrong.

Pi = ~3
3 =/= infinite number

The Lord Slide Rule · November 14, 2014, 11:05:00 AM

Quote from: Flee on November 14, 2014, 10:56:07 AM

Quote from: SexyPiranha on November 14, 2014, 10:43:44 AM
Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM
Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular
Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.
I've been thinking of doing something like that for law stuff, but not much time or motivation.

Sounds interesting, will be looking forward to it should you ever decide to do it.

g💚jira · November 14, 2014, 11:06:16 AM

Quote from: SexyPiranha on November 14, 2014, 10:43:44 AM

Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM
Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular
Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.

You're both better at math than the rest of the forums so it doesn't really matter!

Turkey · November 14, 2014, 11:27:59 AM

Quote from: SexyPiranha on November 14, 2014, 10:43:44 AM

Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM
Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular
Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.

I'm not huge on making threads, either. When I made this thread I was thinking something similar; if people responded well, I'd post more stuff later. Not sure what to cover next though.

rC · November 14, 2014, 11:29:38 AM

stem is for faggots who can't get laid

The Lord Slide Rule · November 14, 2014, 11:36:44 AM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 11:27:59 AM

Quote from: SexyPiranha on November 14, 2014, 10:43:44 AM
Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM
Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular
Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.

I'm not huge on making threads, either. When I made this thread I was thinking something similar; if people responded well, I'd post more stuff later. Not sure what to cover next though.

I'm kind of hoping you might get into some higher math. Although like you said I'm not sure how many views that'd get, it's ultimately up to you.

I was considering doing one over misconceptions about irrationals, what w/ Assassin's comment and all.

Lemy the Lizerd · November 14, 2014, 11:40:38 AM

Math is fucking gay

Sandtrap · November 14, 2014, 11:51:45 AM

Quote from: Lemy the Lizerd on November 14, 2014, 11:40:38 AM

Math is fucking gay

Math is the language of everything m8

The Lord Ruler · November 14, 2014, 12:34:45 PM

Considering I'm only in advanced math, I surprisingly understood all of that.

g💚jira · November 14, 2014, 01:08:51 PM

Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 11:27:59 AM

Quote from: SexyPiranha on November 14, 2014, 10:43:44 AM
Quote from: GodspeedGojira! on November 14, 2014, 10:40:15 AM
Quote from: SexyPiranha on November 14, 2014, 10:34:21 AM
Quote from: GodspeedGojira! on November 14, 2014, 08:11:18 AM
Quote from: Assassin 11D7 on November 14, 2014, 01:33:27 AM
Quote from: E̲n̲ga̲ge̲d̲T̲u̲r̲k̲e̲y on November 14, 2014, 01:27:22 AM
Quote from: Assassin 11D7 on November 14, 2014, 12:47:41 AM
Pi isn't a finite volume. You're maths wrong.

Are you trying to claim that pi isn't constant? Because it certainly is. Just because it's irrational doesn't mean it isn't a finite volume.
Then what's the final decimal of Pi?

Are you seriously trying to make the argument that non terminating numbers are infinite in value?
This thread makes me want to do a series of threads where I *try to help clear up some mathematical misconceptions the non-math plebs have.

Although I'm not sure how many views it'd get.

I'm down for it. You and Turkey Math-ifying the Serious forums would be spectacular
Tbh turkey'd probably be more suitable for it, not only is he better at math than me, I'm also not much of a thread maker, but I'm willing to give a shot.

I'm not huge on making threads, either. When I made this thread I was thinking something similar; if people responded well, I'd post more stuff later. Not sure what to cover next though.

Something involving cardinality