Koch Snowflake Fractal

[TheFlygt]

It's pronounced koKH, not kosh.

Fractals are very interesting, I would say that is among the easiest of them all.

[KarmaProstitute]

@TheFlygt Actually pronouncing "Kokh" or "Kosh" is just as wrong, it's pronounced "KoR" with some sort of a sharp R, not the rolling R but the one that hurts the top of your mouth.

[TheFlygt]

@KarmaProstitute It's a german surname. The retroflex R you speak of is not correct, it is a gutteral sound similar to how you would pronounce Johann Bach.

[KarmaProstitute]

@TheFlygt Yes... that's exactly what I mean.

[TheFlygt]

@KarmaProstitute Aha :) It's hard to explain in text. I misunderstood the "hurts the top of your mouth" bit, as my dialect uses that very sound.

I'm from Bergen, as far north as you can get on the globe and still hear it. The sound entered the Norwegian language through Bergen during Hanseatic times as it was a major trading point. Still the retroflex "rolling" R is always used outside the west and southwest coast.

[k0reankim]

I wonder where khan learns all this stuff....

[jazzbuckeye]

Could you express this in sigma notation as an infinite series?

[joechamm]

@jazzbuckeye

- If each of the sides is length s, then the original area can be written as A = (1/2)s^2. After the first iteration, we are adding the areas of three triangles, each with area (1/2)(1/3s)^2 = (1/9)A, which gives us A + (1/3)A. You'll notice that after this you add 4 times the number of triangles on each successive iteration, each with area (1/9) the area of the last iteration's triangle(s)... ie you are adding (4/9)^k area on each iteration, giving you a geometric series.

[pnbllwzrd95]

I hope by the island of England you mean Great Britain - (excluding outlying islands such as the Orkney Islands, Shetland islands etc. as they would make it more than one Island) note I use the term Great Britain and not the United Kingdom as that would include Northern Ireland. :)

[artmonger78]

This guy sounds like an older version of Chris (seth green) from family guy... Great vids though.. love me some khan academy

[robsonomasold]

Great sounding voice, very clear and easy to follow. This guys is good.

[778ironman1]

england looks like a boot

[TheBazzalisk]

These videos are great! :)

[EarthsDetour]

Never heard of that before! Although, why do you assume that the coastline stops at the atomic when it is not much so for the original model?

[amoeba909]

Hey Sal,

An interesting conjecture from an amateur physicist (0.0001 on a scale from 0.0001 to 10000000000.000).

Can we bind the universe in n+1 space dimensions? It is quite interesting that time dimension is irrelevant in this observation!

[McTurman]

Webscape: How to learn almost anything for free

[KaiserReich]

Apparently England looks like a penis.

[someonetoogoodforyou]

The total area is A = 2*sqrt(3) * S^2 / 5

[SammyBoi225]

i am going to put an equal lateral triangle....



[yuyo1948]

Es interesante esta posibilidad de aprender sin prisas. ¿Hay en castellano estos videos o subtitulados?

[TheAhmedMAhmed]

thanks .. never thought about it ...

[Pirate44444]

oh yeah, that coast line between England and Wales

[yuyo1948]

Me gustan  y quiero ampliar, pero....hay estos videos es castellano o subtitulados.

[silencedidgood]

Sal talking about fractals....infinite perimeter....finite area. What better way to start the morning in a fractious world.

[sonicpawnsyou]

Aw, khanacademy.

The video would have been so much funnier if you just pronounced it "cock" all the time!

[LoveTehSun]

How is area fixed?

[KarmaProstitute]

@LoveTehSun See that hexagon he drew ? Well you can say for sure "it won't get bigger than that." Now, see the corners of the hexagon ? Eat a little bit of each of the 6 corners (bevel I guess). You get a big 12-side shape, and you can still say (implying you haven't eaten too much) : "the fractal won't get bigger than that". Now keep on doing this, for a time you can, but after a while you *will* have eaten too much of the original hexagon, and you've found a finite area

[LoveTehSun]

@KarmaProstitute Thanks, Karma. That answers my question.

[igorkrupitsky]

Assuming that initial triangle is 1 meter, it would take about 30 iterations to go to down to atomic level.

In Excel type: =POWER(2,-30). Hydrogen Atom size is about POWER(10,−10) m.

[pushupsjono]

@igorkrupitsky Interesting! In reality, would a fractal go on beyond the atomic level? It makes me feel weird that the pattern might go on forever, as if everything is like a video game :p

[scottycatman]

How do I explain this... Well, the area is finite because it's bound in that hexagon. The perimeter is only explained as "infinite" because it's ever-increasing. However, don't think for a second that by "infinite" he means that its perimeter can be in the trillions.

[BurkeyAcademy]

@scottycatman No, it really is Infinite. The shape keeps getting more and more complex at smaller scales, so that you keep needing to add more "string" to outline all of the infinite facets, and you can never keep up. When we say that something is infinite, we never mean "trillions". Trillions are quite small. :)

[scottycatman]

@scottycatman

Y'know what? I forgot to factor in that there are more triangles in each 'tier'... I was going off of the idea that each tier had the same amount of triangles. Thanks for replying, otherwise I wouldn't have second guessed myself.

[scottycatman]

Now I can't sleep at night.

[someonep93]

Correction: Coch -> Koch

[someonep93]

I looked into his family name a bit more and found that the name is pronounced like "kokk" would be pronounced in Swedish (my native language). So, the English pronounciation would be more or less: "cock".

Fun facts: Helge von Coch was born into a family belonging to the Swedish nobility. He studied at Stockholm University under Gösta Mittag-Leffler, another famous mathematician.

[Senakujin]

Hmmm.. still don't see the infinite to finite comparison as very logical. Its like you said in the island example, it works until you go to the atomic level at which point you'll reach a finite perimeter. I guess my argument is that in the real world you'll hit the wall of a immeasurable unit for both perimeter and area. I guess in `theory` you should always have a unit of measurement but eh.. mind will not compute.

[MetalMilitia072583]

its a little after 4am and i was falling asleep... i started watching this and now im wide awake!! go figure....

P.S. i credit khan academy for my A in calculus and preach it to all of my friends

[eksman187]

Koch means cook in german. it is being spelled like you want to spit out ^^

[xmyccymx]

@eksman187 are you partly German?

[PHILANTHROPIST1988]

i cannot imagine what my life would be without khanacademy

thank u very much khan -_-

[porkypine1888]

Yes fractals!!!!!!

[A010795]

lol I love how you repeat the things you say while writing it out :P

[Remaeus]

Where is this on Khan Academy? 

[v12345vtm]

how long is a piece of string -theory ! :)

[jamesjosephclarke]

I always like liked the Menger Sponge, infinite surface area, zero volume.

[personkid20]

earliest "described fractals", oh ye misled Sal, search for Africkan Fractals

something used in Afrikan culture for centuries and some say millenniums.......

[somnys]

@personkid20 do you know what "described" means?

[somnys]

@personkid20 do you know what "described" means?

[personkid20]

@somnys is your name sal?

[personkid20]

@somnys or do you just cook his meals and fold his undies?

[somnys]

@personkid20 Neither. Are you dumb or really dumb?

[LartenAndel]

@somnys

I believe he is in between those two.

[metaldave08096]

Great Video, i read about the Koch snowflake in a book that i have and didn't quite understand it but this cleared everything up perfectly for me!!!

[Lojikish]

So in other words, England owns the universe.

[Freshman000000]

Can you give us the formal proof for the finite area of the Koch Snowflake? For those of us who are far past the basics.

[somnys]

@Freshman000000 if you're really far past the basics, then you should be able to prove it yourself.

[Manodragon]

Can you do more biology videos? They are incredibly interesting :)

[ken25taylor]

I love the work of Dr. Emoto where he flash freezes water after thought experiments on them and the water crystals have a fractal nature. Thanks for the upload!

[lmcdowall]

This is why I love math! Great video!

[KiloSierraAlpha]

Koch is pronounced as "coke".

[Alignn]

@KiloSierraAlpha

A guy I know of, "Johan Koch", has people pronouncing his last name more like cock (as you would a shotgun, say), though neither is quite right (and some dialects pronounce cock more like cack, which is completely off).

[Alignn]

@KiloSierraAlpha

A guy I know of, "Johan Koch", has people pronouncing his last name more like coc (as you would a shotgun, say), though neither is quite right (and some dialects pronounce that word more like cack, which is completely off).

[superdau]

@KiloSierraAlpha

Far from it. But I think it's hard for english speakers since you don't really have the sound of "ch". It's like the "loch" in "Loch Ness" or like the "ch" in "Bach" (the composer).

[ICarnag3I]

What did he major in?

[NewgroundsOwnSBB]

@ICarnag3 everything

[vpletap]

@ICarnag3I

MATH, electrical engineering, and computer science.

[KaHabbful]

@ICarnag3I Salman Khan was valedictorian of his high school class (Grace King High School). Khan holds three degrees from the Massachusetts Institute of Technology: a BS in mathematics, a BS in electrical engineering and computer science, and a MEng in electrical engineering and computer science. He also holds an MBA from Harvard Business School

[Katana221985]

I thought that not P(infinity) is equal to infinity bu the sum of all P's.