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[challenge entry] Using maths to explain...maths


This picture courtesy of Wikipedia proves that 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.

Let’s say the whole area in this picture has an area of 1. Now concentrate on the black squares. The one in the bottom left hand corner is 1/4 of the total area. The next black square is a quarter of the top right hand corner a quarter the size of the biggest black square so 1/16 of the total area. The next one is a quarter again 1/64 and so on. So we know that all of the black squares together are equal to 1/4 + 1/16 + 1/64 + 1/256 + ...

Now look at the grey squares. In total they are the same as the black squares. Similarly the white squares are in the same arrangement as the black squares. We have three identical sequences of squares and when added together they give the total area of 1. Consequently we can conclude each sequence of squares has area 1/3. So 1/4 + 1/16 + 1/64 + 1/256 + ... = 1/3.

I know this isn't funny but it is big and it is clever and I like this sort of thing.

From the Explain Stuff With Maths challenge. See all 249 entries (closed)

(I helped save b3ta! GarbageFan didn't know what to have as a board sig on, Sun 3 Jan 2010, 2:44, archived)
# It's not big, thank fuck,
and it's not that clever either.

Fuck off!
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 2:48, archived)
# This is big, dammit
And really clever too

Welcome to the family.
(I helped save b3ta! zeltergiset, Sun 3 Jan 2010, 2:51, archived)
# This was supposed to be the opposite of sushi's post but now there's a fucking hamster in the middle.
(I helped save b3ta! zeltergiset, Sun 3 Jan 2010, 2:51, archived)
#
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 2:52, archived)
# Thanks bro
This is really good.
(I helped save b3ta! zeltergiset, Sun 3 Jan 2010, 2:53, archived)
# Hahaha. Awesome :)
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 2:54, archived)
# Oh, so now my post was wasted!
Cheers cunt!
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 2:55, archived)
# Here, have a blank one of mine.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 2:55, archived)
#
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 2:55, archived)
# Too fucking late man!
TOO FUCKING LATE!

You have made me so angry now that I am going to listen to RAP MUSIC!

www.youtube.com/watch?v=GXMKmxR3avc
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 2:59, archived)
# Man up and get over it.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:01, archived)
# I AM NOT MAXIMINIUS!
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 3:06, archived)
# I'm still buying a bunny hat when I get the chance.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:10, archived)
# Nice one Furry!
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 3:20, archived)
# You're just jealous of my soon to be awesome ear hat.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:21, archived)
# Really, I'm not.
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 3:25, archived)
# You're either lying or dead inside.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:27, archived)
# Or, and just try this one out for size,
I don't garner pleasure from wearing animal costumes.
(I helped save b3ta! Redsushi! Whoop! Whoop! Yes, that one!, Sun 3 Jan 2010, 3:32, archived)
# It's not a costume, it's a hat with ears.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:58, archived)
# Well, I quite like it
But it is the kind of thing I like.
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 2:53, archived)
# It's okay, don't let sushi dictate the mood
Rage against the whoop
(I helped save b3ta! zeltergiset, Sun 3 Jan 2010, 2:56, archived)
# Fuck you, I won't flame who you tell me.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:01, archived)
# I just found out that a snails anus is closer to its brain than almost all of its other organs.
en.wikipedia.org/wiki/File:Snail_diagram-en_edit1.svg
The fuck is up with that, man.
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 3:03, archived)
# That's the respiratory pore.
(I helped save b3ta! Mu Dinofiddler, Sun 3 Jan 2010, 3:05, archived)
# Pneumostome! >:(
I hate those things. But the annotation above points out the snails anus, which is clearly closer to its brain than the lung, heart, liver, stomach, kidney and foot D:
Wait, scratch that last one.
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 3:08, archived)
# how its know
(I helped save b3ta! Sir Sand GOBLIN ^popular page dis, Sun 3 Jan 2010, 2:56, archived)
# I can take limits herpaderp
(k3b/-\b Peace man., Sun 3 Jan 2010, 3:01, archived)
# No no, no no no no, no no no no, there's no limit
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 3:04, archived)
# I have been ruined by team america
i read "herpaderp" and all my brain said in response was "muhammad jihad"
(I helped save b3ta! arrangedletters, Sun 3 Jan 2010, 4:18, archived)
# I've just had a thought everybody
A "plummet" is a small plum.
(I helped save b3ta! discomeats This canoe, Sun 3 Jan 2010, 3:09, archived)
# I vote for this to be in the next dictionary.
(I helped save b3ta! xihpete A neutrino walks straight through a bar, with v>c., Sun 3 Jan 2010, 3:11, archived)
# In the plural that's "plummets" then
There aren't enough words to describe a gentleman with unusually small plums.
(I helped save b3ta! GarbageFan didn't know what to have as a board sig on, Sun 3 Jan 2010, 3:18, archived)
# So what's a socket?
(I helped save b3ta! mofaha ┐( ˘_˘)┌ ʅ(́◡◝)ʃ, Sun 3 Jan 2010, 3:23, archived)
#
nsfwish
(I helped save b3ta! e1bow parts of this page are not secure, Sun 3 Jan 2010, 3:38, archived)
# something you empty your plums into
(I helped save b3ta! discomeats This canoe, Sun 3 Jan 2010, 4:58, archived)
# i think your profile pic is missing a glass of orange juice and a croissant
*i'll be nice and not shop them on, but i can't be held responsible for any other b3tans actions*
(Rattlehead all time with the gay, forever touching, Sun 3 Jan 2010, 3:10, archived)
# So long as the picture isn't also flipped horizontally we'll know which is the original
(I helped save b3ta! GarbageFan didn't know what to have as a board sig on, Sun 3 Jan 2010, 3:23, archived)
# I will kill again.
(I helped save b3ta! mofaha ┐( ˘_˘)┌ ʅ(́◡◝)ʃ, Sun 3 Jan 2010, 3:23, archived)
# that's
your answer to everything
(I helped save b3ta! Dr Scunner She’s a he, technically, but she’s scalding hot, Mon 4 Jan 2010, 13:37, archived)
# Shirley Manson can't make music
Your maths is wrong
And Buffy was a whore


Books are ok though.
(I helped save b3ta! thiswasmyclone, Sun 3 Jan 2010, 3:32, archived)
# tl;dr
(I helped save b3ta! Ttssattsr, Sun 3 Jan 2010, 4:44, archived)
# I think you actually make a valid point about science
as you can see, using mathematics to explain something which is allready expressed in mathematics just digs us further and further away from reality. likewise, we can move backward through the same fractal explaining abstract concepts using everyday objects and closer and closer to real.

It is all inside itself and outside itself simultaneously.

Narim hassein explains this in his 'fractal universe' lectures; here
Though, he's not a scientist.
(lunatek, Sun 3 Jan 2010, 15:21, archived)
# Oh god, not him again.
As far as I can tell he's just doing his best to misunderstand and jam together random bits of science he's read. Probably while stoned.

Now for a REAL fractal universe theory check out Laurent Nottale and his "Scale Relativity".
(I helped save b3ta! the wub - guide onion for the blind, Mon 4 Jan 2010, 21:05, archived)