@SamwizeTheBrave1 i'm in silly 10th grade geometry. pqrd3's reply cleared up any confusion i had. These guys are very good teachers. I'm still not sure how proving a # impossible makes it... an impossible #
why can't they be two even numbers? what about four over two or any even number over two? I think the last bit wasn't explained properly, can somebody help me here?
@upbeatanime Because if they are both even numbers they can be written in a lower form. Like 2/4 is the same as writing 1/2, which is the lowest way (using integers) of writing one half. The problem is that they started off by saying that a/b is written as two integers in lowest terms, so both a and b being even contradicts this.
@upbeatanime A/B is meant to be the root of 2 in it's smallest possible form (Like 1/2 is a half in it's smallest possible form) in it's smallest possible form, a fraction has one even number and one odd number which that equation doesn't have, therefore the fraction is impossible
@upbeatanime a/b is meant to be in lowest possible terms, so its not 2a/2b.Thats a premise of the problem.
it's like getting 2/4 instead of 1/2 as the lowest simplification. no sense made. if both # are even,then they can both be divided by 2,and therefor, are not the lowest possible digit-even though it is...making it impossible...i think.
@RittervonSt So what you're saying is that you can create irrational numbers simply by taking ratios between non-integers? It sounds like that's what you're saying...
The ration of the long side/short side of A4 paper is really really close to the square root of 2.
The thing is, you can never ever get the actual value of the square root of 2 with division. The square root of 2, or 3 or 5... or pi are irrational number so you can only come infinitely close to it with division, but never actually reach it.
LOL. I did this A4 ratio calculation when I was in high-school. Not as an assignment but by myself as a entertaining puzzle. I only now realize I what I was doing. Got into art though, not in maths. Still aiming for my own desert island though. ;^)
@nopuelbmuts The fact that the ratio is not a rational number does not mean that it cannot be made precisely. To illustrate this, consider that you have a square of paper that is exactly one meter by one meter. Then consider that you cut the square of paper perfectly straight from one corner to the opposite corner. This would create two triangles of paper, with two sides of each triangle being one meter, and the side along the edge that you cut being the square root of two meters.
Well then didnt you contradict your self when talking about how the sides of the paper divided equals root 2 but then saying that root 2 cannot be written as a fraction or am i missing something?
@putty119 He made a mistake (or was just unclear) with his definitions (he's proving the \sqrt 2 is not a real number: A number that can be written as a fraction in the form of m/n where m and n are integers.)
So technical you are correct depending on what definition you use, because in reality I can write any number as fraction or ratio with a denominator as 1.
you cant prove that b is even just by saying that a=2c. you could have made a equal to any number. for example, if you made a equal to 3c, you would not come up with an even number.
@platinumpikachu13 You must remember the explicit restrictions he placed on the variables at the start of his proof and remember some important definitions:
a and b are integers and in reduced form: if a and b are separately divided by any number the result must not be an integer
Even number: An integer that is divisible by 2 giving a integer quotient.
@jonesmm3 wait youre right! If you can get the long side of a paper divided by the short side to equal √2 then you are indeed writing it as a fraction. What the heck.. what am i missing in my understanding of this.
@blackout2240 The thing is that the length of a side of paper is not limited to integer ;) You see - in the proof we assumed that a and b are integers, so we proved that sqrt(2) can not be written as a fraction of integers. No one said anythign about decimal numbers :)
@TheScars75 They'd have to piss northwards if they live north of the Tropic of Cancer, southwards if they live south of the Tropic of Capricorn, or northwards or southwards depending on the time of year if they live between the Tropics.
@TheScars75 The sun can pass directly overhead, or underfoot, in the tropics, and the tropic of cancer is way down in Africa; which was how Eratosthenes was able to calculate the shape and size of the Earth, though that was several hundred years later.
Uh, that is what the professor said, so why the objection? Pantheism is the view that God is the universe, or that God expresses himself as the universe. The Catholic church did not like this theory due to their assumption that God must be separate from the universe, but Giordano's view left no room for God thus he was burned for his pantheistic view that the universe is infinite.
@ObadiahtheSlim Uh, that is what the professor said, so why the objection? Pantheism is the view that God is the universe, or that God expresses himself as the universe. The Catholic church did not like this theory due to their assumption that God must be separate from the universe, but Giordano's view left no room for God thus he was burned for his pantheistic view that the universe is infinite.
My question is: How did you figure a=2c why can't it be a=3c
sorry if that question sounds a bit stupid, but if a=3c then b^2 doesn't necessarily have to be even, so it's pretty important that a=2c for this video to be true.
@commetsmasher Because a has to be even and any even number can be written as 2 times some integer (in this case c)...so if a was 2 then c would be 1, if a was 14 then c would be 7, if a was 2680 then c would be 1340, and so on, so any even number a can be written as the product of 2 and some other integer (2c), that obviously is not true for 3c since any odd value for c would make a odd, which is not allowed.
@MysteryR000 No, if you do this for sqrt(4) you get 4=a^2/b^2 then 4*b^2=a^2, do the substitution for a to get 4*b^2=(2c)^2=4*c^2 which yields the result b^2=c^2, b and c are both positive integers so b=c=0.5*a so a/b=2.
@TheJMan211 Yes, but the point is that if lets say we are trying to disprove sqrt(3) it would NOT be an even number, but one divisible by 3. Plus, if a/b = 4 then how did you get a/b = 2?
OK, ok, ok, for all you over-analytic jerks (@SupGaillic @Zfernbaugh@LoudTristero), I recently stated that "the square root of any number is irrational", which is only half wrong. I accidentally disregarded the existence of perfect squares. What I meant to say was that you can not express the square root of 2 as a fraction, because it is irrational.
How can the ratio between the two side of paper be the square root of two if that is impossible? That would also mean that there is no ratio that stays the same when you would fold the paper in half.
@pielover267 Because in reality the ratio between the sides of A0 (or A-whatever) paper approximates sqrt(2). A0 paper is 1189x841 mm, so 1189/841=1.41379... whereas sqrt(2)=1.41421... The ideas is that the ratio should be sqrt(2), but then by defining the lengths of both edges of the paper as integers, they only make the ratio close to sqrt(2). But still, if you fold A0 paper in half 8 times then round it to get A8 paper (74x52mm), it's still 74/52=1.423..., which is really close to sqrt(2).
Hey bub guess what: the square root of any number is irrational, meaning that any irrational number can not be accurately expressed as a fraction. The ratio of the longest and shortest edge of that piece of paper may be approximately equal to the square root of 2. in this video you say "will be the square root of 2." That is an untrue statement. Case closed
It's correct, instead of using .5 a^2, both sides were multiplied by two (or divided by.5 if you have no soul). So, instead of .5a^2=b^2, it is a^2=2b^2.
Also, .5a*a=.5a^2, I think that was your main problem, look up the commutative property if you need to know why.
@thutama That's because it isn't made in the A size ratio. Not all paper is made the same. He was saying that all the A scale paper goes with the ratio of root 2, not all paper is.
i like how the first half of this video tells us that the sides of paper have a ratio of root 2, and the second half of the video tells us that there are no numbers that have a ratio of root 2
I have a hard time imagining a length being defined as something that has an infinite number of decimal places so that you can never have a definite length, even though it's bound between the two sides with lengths of 1.
@ifajig1 Because in school, you don't learn about math, you mostly learn about computation. There are not more than a hand full of proofs I remember from school. Math is beautiful in itself, but math in school scares many people, because you are teached to apply rules while not knowing where they come from. At least that's my experience. It got so much better in university.
@Dasagriva1 Don't be sorry---I make mistakes all the time. Brady does not allow us to have scripts so that I have no idea what I am going to say and somethings come out garbled. Usually he cuts them out. Hope you approve of the rest of the video.
@InvinciblEddy simple: lets get an odd number a. Since a is odd we can express it as (2*b+1). Now we square a and get a² = 4b²+1+2b now we express 2b as c, c is an even number. Now we express 4*b² as d. d is also an even number. Now add d+c+1 and you get a². Since d and c are even d+c has to be even and c+d+1 has to be odd. q.e.d. :)
@InvinciblEddy if you square an odd number, you will get an odd answer (3 squared = 9, 5 squared = 25, 7 squared = 49). if you square an even number, you will get an even answer (2 squared = 4, 4 squared = 16)
It makes sense that there you can find paper sizes A0 (no folds/orignal) through A8 (8 folds from orignal) since you can never fold any size of paper of any thickness more than 8 times.
@coolguty Someone did! Look up "Britney Gallivan" on wikipedia. (You're right that this was the conventional wisdom when those standards were put down, of course).
It goes 997 998 999 1000 1001. But we need to reduce these to 3 digit strings, so we start with the last one, moving the first 1 into the 0 from 1000, we get 997 998 999 1001 001. Next we move the 1 from 1001 into the last 9 in 999, giving us 997 998 1000 001 001. We do this one more time and we get 997 999 000 001 001. If we continue on, the last 001 will become 002, and so on until we get to 997 again, where we'll encounter the 2000 problem and skip again.
So if root to is irrational then why does the the paper end?
skyvb1 5 hours ago
@skyvb1 That has got to be one of the most stupid questions I have seen.
nicevidugotthere 1 hour ago
Well to be exactly truthful when you took the square root of 2 you would have gotten plus or minus the the square root of 2
pendalink 7 hours ago
i cant be the only one who doesnt understand this
SamwizeTheBrave1 22 hours ago
@SamwizeTheBrave1 i'm in silly 10th grade geometry. pqrd3's reply cleared up any confusion i had. These guys are very good teachers. I'm still not sure how proving a # impossible makes it... an impossible #
IronAnimation 8 hours ago
why can't they be two even numbers? what about four over two or any even number over two? I think the last bit wasn't explained properly, can somebody help me here?
upbeatanime 1 day ago
@upbeatanime Because if they are both even numbers they can be written in a lower form. Like 2/4 is the same as writing 1/2, which is the lowest way (using integers) of writing one half. The problem is that they started off by saying that a/b is written as two integers in lowest terms, so both a and b being even contradicts this.
pqrd3 1 day ago 14
@pqrd3 thanks, it makes sense now.
upbeatanime 1 day ago
@upbeatanime A/B is meant to be the root of 2 in it's smallest possible form (Like 1/2 is a half in it's smallest possible form) in it's smallest possible form, a fraction has one even number and one odd number which that equation doesn't have, therefore the fraction is impossible
gta4megafan 9 hours ago
@gta4megafan thanks, i didn't know that before.
upbeatanime 9 hours ago
@upbeatanime a/b is meant to be in lowest possible terms, so its not 2a/2b.Thats a premise of the problem.
it's like getting 2/4 instead of 1/2 as the lowest simplification. no sense made. if both # are even,then they can both be divided by 2,and therefor, are not the lowest possible digit-even though it is...making it impossible...i think.
IronAnimation 8 hours ago
But the side lengths of A4 paper does not come to an integer; If you measured it u will see that there are decimals.
LOLuniverse08 1 day ago in playlist Uploaded videos
2 divided by the square root of 2 equals the square root of 2. Does that make you mad?
meteoryoshi 1 day ago
@meteoryoshi He specifically said whole numbers. Root 2 isn't a whole number.
Blahhikablah 1 day ago
This video is better than sex.
Jebus4377 1 day ago
6:05 ashume :P
driftmcvey19 1 day ago
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driftmcvey19 1 day ago
my brain just got raped
nalby92 1 day ago
@jonesmm3 A peace of paper has not two whole numbers as their side lenghts, therefore everything they said is right :-)
RittervonSt 1 day ago
@RittervonSt So what you're saying is that you can create irrational numbers simply by taking ratios between non-integers? It sounds like that's what you're saying...
jonesmm3 1 day ago
Please explain why a is an even number.
BFuhrH 1 day ago
4 and evil numbers ;)
theoffkeydiva 1 day ago
@TheScars75 They don't, they waited until it's 12:01
imb3d0r 1 day ago
The proof shown at the end is my all time favorite proof ever done in the field of mathematics.
maqhem 1 day ago
SUPPORT KONY 2012
ojjy123 1 day ago
Mum, i am being educated on youtube...
StealthlyPotato 1 day ago 60
The ration of the long side/short side of A4 paper is really really close to the square root of 2.
The thing is, you can never ever get the actual value of the square root of 2 with division. The square root of 2, or 3 or 5... or pi are irrational number so you can only come infinitely close to it with division, but never actually reach it.
Ration of A4 paper: 1.414285714...
Square root of 2: 1.41421313562...
close enough
Misteryman94 1 day ago
This has been flagged as spam show
!!!!!!!!!! Kony 2012 !!!!!!!
hapasine1 1 day ago
I have to say, as far as cults go, a math centric one seems preferable to... well any other kind
outsider344 1 day ago in playlist Uploaded videos
LOL. I did this A4 ratio calculation when I was in high-school. Not as an assignment but by myself as a entertaining puzzle. I only now realize I what I was doing. Got into art though, not in maths. Still aiming for my own desert island though. ;^)
PuppyZwolle 1 day ago
you could also have negitive root 2
chattyw87 1 day ago
why do they always use brown paper and not whiteboards?
thcoolman1 2 days ago
somebody stop him he's going to get a paper cut
spankmyhair1 2 days ago
Math > sleep > Algebra 2 homework
<3
stertheder 2 days ago
Golden Ratio! sorta
FlamingSpaz29 2 days ago
no more markers on paper!!
Kenwric 2 days ago
MY BRAIN HURTS WHICH MEANS I AM SUBBED
MrGigs94 2 days ago
You could also find out that it would be the square root of 2 by using the special triangle that it will always be, or at least for the 1x1 triangle.
TheDarkbytes 2 days ago
I live in America where we traditionally use 8.5" x 11" paper. Is this video relevant to me or did I just misunderstand it?
WolfgangNS 2 days ago
To root one is fine, to root two is totally irrational.
dubaipete 2 days ago
@dubaipete Don't even get me started on root NEGATIVE one :P
maulingunow 2 days ago
If root 2 cannot be written as a fraction, then what is the length and width of A4 paper, since the length over the width = root 2?
nopuelbmuts 3 days ago
@nopuelbmuts It isn't exactly root 2, but it is somewhat close, I'm guessing.
IamGumbyy 3 days ago
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FarnhamJ07 2 days ago
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FarnhamJ07 2 days ago
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@nopuelbmuts The fact that the ratio is not a rational number does not mean that it cannot be made precisely. To illustrate this, consider that you have a square of paper that is exactly one meter by one meter. Then consider that you cut the square of paper perfectly straight from one corner to the opposite corner. This would create two triangles of paper, with two sides of each triangle being one meter, and the side along the edge that you cut being the square root of two meters.
FarnhamJ07 2 days ago
Never thought I would hear a number described as "sordid"!
Faren22 3 days ago
the younger guy is too patronizing! other than that it is a good vid!
deggerzz1 3 days ago
@deggerzz1 I don't agree. Enthusiastic yes, patronizing no. Please check other videos in this series, then see if you still think the same. peace.
dubaipete 2 days ago
Well then didnt you contradict your self when talking about how the sides of the paper divided equals root 2 but then saying that root 2 cannot be written as a fraction or am i missing something?
putty119 4 days ago
@putty119 He made a mistake (or was just unclear) with his definitions (he's proving the \sqrt 2 is not a real number: A number that can be written as a fraction in the form of m/n where m and n are integers.)
So technical you are correct depending on what definition you use, because in reality I can write any number as fraction or ratio with a denominator as 1.
Q3020Q 4 days ago
you cant prove that b is even just by saying that a=2c. you could have made a equal to any number. for example, if you made a equal to 3c, you would not come up with an even number.
platinumpikachu13 5 days ago
@platinumpikachu13 You must remember the explicit restrictions he placed on the variables at the start of his proof and remember some important definitions:
a and b are integers and in reduced form: if a and b are separately divided by any number the result must not be an integer
Even number: An integer that is divisible by 2 giving a integer quotient.
even^(2) = even
odd^(2) = odd
We rearrange to: a^(2) = [ b^(2) ] / 2
Therefore b must be even.
Q3020Q 4 days ago
HIS MARKER SAYS A! MINDFUCK!
TheSSBOABand 5 days ago
@numberphile can a "contradiction" also be called an indirect proof?
MagnetiXofficial 5 days ago
singing banana :P
lennic95 5 days ago
3:22 Nice pronunciation.
xxDARKSWORD929xx 5 days ago
"The sqRuare Root of 2" thats adorable.
sm0kingJay 5 days ago
So what was shown at the end proves absolutely that the A series of paper is a lie.
jonesmm3 5 days ago 35
@jonesmm3 no, because a and b at 3:00 dont have to be integers. so a/b is not a fraction, just two numbers divided
Meggax1 1 day ago
@jonesmm3 No, it shows why the length and width of the A series of paper are not whole numbers.
RellikDesign 1 day ago
@RellikDesign *the ratio of length and width.
Mrgreenblacksoul 1 day ago
@jonesmm3 and why is that?
angello90pl 1 day ago
@jonesmm3 wait youre right! If you can get the long side of a paper divided by the short side to equal √2 then you are indeed writing it as a fraction. What the heck.. what am i missing in my understanding of this.
blackout2240 1 day ago
@blackout2240 The thing is that the length of a side of paper is not limited to integer ;) You see - in the proof we assumed that a and b are integers, so we proved that sqrt(2) can not be written as a fraction of integers. No one said anythign about decimal numbers :)
lvojnovic 19 hours ago
@lvojnovic ah, as i figured after i thought about it for a while. thanks for the reply
blackout2240 7 hours ago
A4 paper is 8.5 x 11. 11 / 8.5 = 1.2941 ...
Fold it in half 8.5 / 5.5 = 1.54 ...
Fold it in half 5.5 / 4.25 = 1.2941 ...
While it may have a predictable series of out comes, it does not always (ever) equal root 2 (1.4142 ... )
Dakktyrel 6 days ago
@Dakktyrel Sorry to inform you that the official dimensions for A4 paper is 8.3 x 11.7 in
and true it doesn't exactly equal root 2, however, it is extremely close.
11.7/8.3 = 1.409638...
root 2 = 1.414213...
JFlopex 6 days ago
@Dakktyrel That's what he said, that rad(2) was impossible to represent as a fraction.
pixeltunechip 6 days ago
I'm disappointed. I thought this was going to be really complex -_-
TheDigitalStone 1 week ago
i thought this was possible with the golden ratio too? hmm
GreenEggism 1 week ago
Do one about Galileo's paradox.. Mind blowing!
vinivinus 1 week ago
I wonder what the bikers thought when they saw the guy explaining root 2
brianduckywelsh 1 week ago
forehead vagina.
OutoftheblueNinja 1 week ago
In which direction are they supposed to piss at noon?
TheScars75 1 week ago 100
@TheScars75 As long as they aren't lying on their backs I think they're good.
fantaboyvideo 6 days ago
@TheScars75 I guess any direction but 'up' is fine :)
anaikahas 5 days ago
@TheScars75 The sun is "up" right? Well don't piss up. Answer solved.
The real question is what to do when your toilet faces east or west. What am i supposed to do now? :)
gredangeo 5 days ago
@TheScars75 They'd have to piss northwards if they live north of the Tropic of Cancer, southwards if they live south of the Tropic of Capricorn, or northwards or southwards depending on the time of year if they live between the Tropics.
RadRafe 4 days ago
@TheScars75 Simple, you don't piss at noon.
Blackops981 4 days ago
@TheScars75 Depends which hemisphere you're in.
Crushermach3 3 days ago
@TheScars75 The sun can pass directly overhead, or underfoot, in the tropics, and the tropic of cancer is way down in Africa; which was how Eratosthenes was able to calculate the shape and size of the Earth, though that was several hundred years later.
Aletheophile 2 days ago
@TheScars75 Towards Mecca?
Digimaul 2 days ago
@TheScars75 lying face down. ;P
danielth 2 days ago
@TheScars75 any direction except up
LukeLAMMan 2 days ago
@TheScars75 Not up! :3
stertheder 2 days ago
@TheScars75 Certainly not up
midgetman9942 2 days ago
@TheScars75 straight down!
maxgrubb 2 days ago
@TheScars75 Straight down?
SwiiTcHBacKPs3 1 day ago
@TheScars75 exactly to the ground at a 90 degree angle
Toiletclottingpoop 1 day ago
@TheScars75 Hold it.
theoffkeydiva 1 day ago
OBJECTION! Giordano Bruno was burned at the stake for heresy stemming from his pantheistic views.
ObadiahtheSlim 1 week ago
@ObadiahtheSlim
Uh, that is what the professor said, so why the objection? Pantheism is the view that God is the universe, or that God expresses himself as the universe. The Catholic church did not like this theory due to their assumption that God must be separate from the universe, but Giordano's view left no room for God thus he was burned for his pantheistic view that the universe is infinite.
draver21 1 week ago
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@ObadiahtheSlim Uh, that is what the professor said, so why the objection? Pantheism is the view that God is the universe, or that God expresses himself as the universe. The Catholic church did not like this theory due to their assumption that God must be separate from the universe, but Giordano's view left no room for God thus he was burned for his pantheistic view that the universe is infinite.
draver21 1 week ago
My question is: How did you figure a=2c why can't it be a=3c
sorry if that question sounds a bit stupid, but if a=3c then b^2 doesn't necessarily have to be even, so it's pretty important that a=2c for this video to be true.
commetsmasher 1 week ago
@commetsmasher Because a has to be even and any even number can be written as 2 times some integer (in this case c)...so if a was 2 then c would be 1, if a was 14 then c would be 7, if a was 2680 then c would be 1340, and so on, so any even number a can be written as the product of 2 and some other integer (2c), that obviously is not true for 3c since any odd value for c would make a odd, which is not allowed.
TheJMan211 1 week ago in playlist Uploaded videos
@TheJMan211 ok, that makes sense! Thanks, this helped a lot :)
commetsmasher 1 week ago
Wait, but if you do sqrt(4), can't it also be disproved, even though it can be written as a fraction?
MysteryR000 1 week ago
@MysteryR000 No, if you do this for sqrt(4) you get 4=a^2/b^2 then 4*b^2=a^2, do the substitution for a to get 4*b^2=(2c)^2=4*c^2 which yields the result b^2=c^2, b and c are both positive integers so b=c=0.5*a so a/b=2.
TheJMan211 1 week ago in playlist Uploaded videos
@MysteryR000 and that doesn't prove that b is even
TheJMan211 1 week ago in playlist Uploaded videos
@TheJMan211 Yes, but the point is that if lets say we are trying to disprove sqrt(3) it would NOT be an even number, but one divisible by 3. Plus, if a/b = 4 then how did you get a/b = 2?
MysteryR000 1 week ago
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OK, ok, ok, for all you over-analytic jerks (@SupGaillic @Zfernbaugh @LoudTristero), I recently stated that "the square root of any number is irrational", which is only half wrong. I accidentally disregarded the existence of perfect squares. What I meant to say was that you can not express the square root of 2 as a fraction, because it is irrational.
drizzy8450 1 week ago
...there's a book called "The Square Root of 2." It has a green cover, yellow binder, orange back cover, and is authored by David Flannery.
jwmmath 1 week ago
irrational = not RATIOnal, not not rational
NewgroundsOwnSBB 1 week ago
:brilliant:
yesdog88 1 week ago
Please no more markers on paper, please for the love of Christ!
Beannaich 1 week ago
These guys make me hate math way less.
punkassbamboo 1 week ago
lol, it seems infinity is an even number....
masluxx 1 week ago
@masluxx even numbers are intigers, which are rational numbers. We cannot describe infinity as a ratio.
purr80002 1 week ago
How can the ratio between the two side of paper be the square root of two if that is impossible? That would also mean that there is no ratio that stays the same when you would fold the paper in half.
pielover267 1 week ago
@pielover267 Because in reality the ratio between the sides of A0 (or A-whatever) paper approximates sqrt(2). A0 paper is 1189x841 mm, so 1189/841=1.41379... whereas sqrt(2)=1.41421... The ideas is that the ratio should be sqrt(2), but then by defining the lengths of both edges of the paper as integers, they only make the ratio close to sqrt(2). But still, if you fold A0 paper in half 8 times then round it to get A8 paper (74x52mm), it's still 74/52=1.423..., which is really close to sqrt(2).
deyv87 1 week ago
11 / 8.5 = 1.29411765
square root(2) = 1.41421356
Close but no cigar.
erik4727 1 week ago
@erik4727 A4 is not 8.5 X 11, that's american paper.
Zfernbaugh 1 week ago
still don't believe me? BAM!!!
h t tp: // w w w. mathsisfun. com / irrational - numbers . html
drizzy8450 1 week ago
@drizzy8450 From that website, right under the golden ratio:
"But √4 = 2 (rational), and √9 = 3 (rational) ...
... so not all roots are irrational."
Zfernbaugh 1 week ago
Hey bub guess what: the square root of any number is irrational, meaning that any irrational number can not be accurately expressed as a fraction. The ratio of the longest and shortest edge of that piece of paper may be approximately equal to the square root of 2. in this video you say "will be the square root of 2." That is an untrue statement. Case closed
drizzy8450 1 week ago
@drizzy8450 Except for like... 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169... to name a few.
LoudTristero 1 week ago
@drizzy8450
√256 = 16
√16 = 4
√4 = 2
SupGaillac 1 week ago
I love your videos :D
DrHipeeMan 1 week ago
MINDFUCKED.
PoopTruffles 2 weeks ago 64
@PoopTruffles i am in sixth grade and i kind of understand this because i love math but other than that, MINDFUCKED.
MrDudeer 3 days ago
@MrDudeer That was completely called for. (sarcasm)
PoopTruffles 3 days ago
@PoopTruffles what do you mean? i was agreeing wit you not being mean
MrDudeer 3 days ago
@MrDudeer o__o
PoopTruffles 3 days ago
a/b = b/0.5a
This does not equal a^2 = 2b^2.
The reason is because your second fraction is 0.5a, so how did you get a^2? Did you throw away the 0.5? (by 0.5, im referring to 1/2 times a)
I'm no wiz in Math, so please dont be upset if this is a dumb question.
thewanderer916 2 weeks ago
@thewanderer916 you get 0.5a^2 = b^2. If you divide both sides by 0.5, you get a^2 = 2b^2. C'mon guy, it's simple arithmetic.
averagejoe91741072 2 weeks ago
This has been flagged as spam show
@thewanderer916 0.5 on the bottom of a fraction is the same as 2 on the top. thus a^2=2b^2
touzaniatw 2 weeks ago
@thewanderer916
It's correct, instead of using .5 a^2, both sides were multiplied by two (or divided by.5 if you have no soul). So, instead of .5a^2=b^2, it is a^2=2b^2.
Also, .5a*a=.5a^2, I think that was your main problem, look up the commutative property if you need to know why.
bamman62 2 weeks ago
wait i was watching futurama HOW THE- o nevermind
Roxas6674 2 weeks ago
ISO 216, heck yeah!
TasnuArakun 2 weeks ago
My number hurts.
ImTheBatchMan 2 weeks ago
A4 . . . mmm not in north america we have letter sized paper which is a bit smaller than A4
thutama 2 weeks ago
@thutama That's because it isn't made in the A size ratio. Not all paper is made the same. He was saying that all the A scale paper goes with the ratio of root 2, not all paper is.
bigglessy 2 weeks ago
i like how the first half of this video tells us that the sides of paper have a ratio of root 2, and the second half of the video tells us that there are no numbers that have a ratio of root 2
jarchibald14 3 weeks ago
@jarchibald14 Because it's an infinite number. The ratio won't be exactly root 2, it's like 1.41 or some other approximation.
bigglessy 2 weeks ago
@jarchibald14 It's about fractions of integers, a should be an integer, b should be a positive integer. That's how the rational numbers are defined.
Jinmago 2 weeks ago
@jarchibald14 There are no INTEGERS that have a ratio of root 2 :)
conartist1991 2 weeks ago
B = c*radical(2)...congrats on the infinite loop contradiction otherwise known as a pardox. You proved nothing.
Veeto1337 3 weeks ago
I have a hard time imagining a length being defined as something that has an infinite number of decimal places so that you can never have a definite length, even though it's bound between the two sides with lengths of 1.
MrJepcats 3 weeks ago in playlist Uploaded videos
@MrJepcats
after about 5 decimals or so the rest just become meaningless, because they mean so little...
Thingie5 3 weeks ago
Too many Numberphile vids in a row makes Homer go something something...
clownstangler 3 weeks ago in playlist Uploaded videos
I am wondering how I can be so fascinated by something I understand so little of...
johann1138 3 weeks ago
2+2=4. Can I join you'll club now?
chrisfowler623 4 weeks ago
heres a cool thing about radical 2:
if you have a square, the diagonal is always "radical 2"(w)
w being the width
figisligit 4 weeks ago in playlist Uploaded videos
somebody tell me why im watching math videos outside of class. and why am i interested...?
ifajig1 1 month ago
@ifajig1
me too XD this seems much more interesting than math class...
Thingie5 3 weeks ago
@ifajig1 Because in school, you don't learn about math, you mostly learn about computation. There are not more than a hand full of proofs I remember from school. Math is beautiful in itself, but math in school scares many people, because you are teached to apply rules while not knowing where they come from. At least that's my experience. It got so much better in university.
Jinmago 2 weeks ago 3
A0 is a meter squared ? Now I know why americans have something else :)
epinardscaramel 1 month ago in playlist Uploaded videos
Root(2) / 1.
BAM.
Root(2) written as a fraction!
gh4ever101 1 month ago
@gh4ever101 Haha. :P Nice. Fraction implies integer numerator and integer denominator though.
Exfenestracide 3 weeks ago in playlist Uploaded videos
@Exfenestracide *Sigh* I kind of figured that, sadly. :/
gh4ever101 3 weeks ago
@gh4ever101 think they're looking for a fraction of integers...
TheJMan211 1 week ago in playlist Uploaded videos
what if a = c^2
purpleguy222 1 month ago
Giordano Bruno, not Bruno Giordano, sorry to say...
Dasagriva1 1 month ago
@Dasagriva1 Don't be sorry---I make mistakes all the time. Brady does not allow us to have scripts so that I have no idea what I am going to say and somethings come out garbled. Usually he cuts them out. Hope you approve of the rest of the video.
MrOldprof 1 month ago
The best thing about the Numberphile videos? There is a promise of an infinite number of them!
otakucode 1 month ago
7:32 - two odd numbers squared makes an odd number? I don't understand that :/
InvinciblEddy 1 month ago
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esylvus 1 month ago in playlist Uploaded videos
This has been flagged as spam show
@InvinciblEddy simple: lets get an odd number a. Since a is odd we can express it as (2*b+1). Now we square a and get a² = 4b²+1+2b now we express 2b as c, c is an even number. Now we express 4*b² as d. d is also an even number. Now add d+c+1 and you get a². Since d and c are even d+c has to be even and c+d+1 has to be odd. q.e.d. :)
esylvus 1 month ago in playlist Uploaded videos
@InvinciblEddy 3^2 = 3*3 = 9 > odd
2^2 = 2*2 = 4 > even
an even number can never be turned into an odd number by multiplying with any whole number
EagleDarkX 1 month ago
@InvinciblEddy if you square an odd number, you will get an odd answer (3 squared = 9, 5 squared = 25, 7 squared = 49). if you square an even number, you will get an even answer (2 squared = 4, 4 squared = 16)
HELLJUMP3R7 3 weeks ago
talk about the gold number
JABRANE4 1 month ago
It makes sense that there you can find paper sizes A0 (no folds/orignal) through A8 (8 folds from orignal) since you can never fold any size of paper of any thickness more than 8 times.
Try it out yourself :)
coolguty 1 month ago
@coolguty Someone did! Look up "Britney Gallivan" on wikipedia. (You're right that this was the conventional wisdom when those standards were put down, of course).
BakerBritt 1 month ago in playlist Uploaded videos
@BakerBritt ahhhh, I had thought of toilet paper. Thanks mate ;)
coolguty 1 month ago
@coolguty And again, Britney Galliven demonstrated that toilet paper can be folded in half twelve times, not eight. :)
Yunituber 1 month ago
Comment removed
nmuller789 1 month ago
hey numberphile, did you know 1/998001 is 0.000 001 002 003 004 005 006......... all the way to 996 997 999 and then repeats with 001 002 003
idk why but it DOES skip 998.
thumbs this up so he and others can see this amazing math discovery!
AtactHD 1 month ago in playlist Uploaded videos
@AtactHD sorry but this is not amazing at all.... you can easily find such numbers...
esylvus 1 month ago in playlist Uploaded videos
@AtactHD
It goes 997 998 999 1000 1001. But we need to reduce these to 3 digit strings, so we start with the last one, moving the first 1 into the 0 from 1000, we get 997 998 999 1001 001. Next we move the 1 from 1001 into the last 9 in 999, giving us 997 998 1000 001 001. We do this one more time and we get 997 999 000 001 001. If we continue on, the last 001 will become 002, and so on until we get to 997 again, where we'll encounter the 2000 problem and skip again.
vampiracy 1 month ago
@vampiracy Nice expanation. 1/998001 is a Carousel number with a repetition length of 998000.
MrOldprof 1 month ago