The square root of two is a fascinating number with a long and sordid history. It also forms the basis of most office paper, such as A4, A3, etc.

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This video features Professor Roger Bowley and Dr James Grime.

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## 43 Comments

Add Yours →Hey, Dr Grime! I believe what you showed us to be "A4" was in fact A3, and "A5" looked like A4! Right?

Soooo…….urinate OPPOSITE the sun! Got it!!!!

so the existence of all my A4 blank papers isnt possible!!!! THEY PUT SOMETHING IN THE WATER !!!!

How can the long side divided by the small side equal sqrt(2)? sqrt(2) is irrational which means no two integers a and b can divide such that a / b = sqrt(2). The A paper series has nothing to do with the sqrt(2)

so then b(i^2)={M/x +c} root 2 ?

Why you have a сyrillic Д on your felt pen?

a=rt(2)(b)

☹️😞

Because a number goes on infinitely you drown the person who discovered that? It's not his fault Lol.

BURNING QUESTION!! how is a times half an a = a squared???

a/b=√2

Wait,that's illegal.

I'm conducting an experiment in neural bio-chemistry & math. Math is a terrible subject for me but I'm going to watch a large swathe of these videos & see if it will improve my skill through immersion. Sixty Symbols & PTV improved my general scientific knowledge greatly.

can anyone explain what happened after 8:23 ? Why are a and b both being even contradictory to our initial assumption?

If you have an irrational number that extends out to infinity wouldn't you therefore have an infinant amount of repetitions

Ehm so you can't express the square root of 2 in a fraction but at the start he said, when you divide the one side of any "a" paper by the other side of the paper then you get the square root of 2, wouldn't that be a fraction ?

With root 2 being irrational, I wonder to how many decimal places the length and width of an A4 sheet of paper are accurate? If we can't get to the last digit of root 2, is it correct that we also can't get to the last digit of what the precise measurements of both the length and width of the sheet would need to be in order for one divided by the other to give root 2?

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Number:

existsDr. Grime: oimmah noot

can you write it as 297/210?

from egypt , we have new Scientist he Explain It To Us In He's Program Its ( El daheeh ) Mr : Ahmed El ghandour i understand it from him ,Easily regardless of your explanation with all respect <3

The basic problem with this proof is that the formulation "let √2=a/b where a and b are both integers and a/b is in simplest terms" is a combination of three separate conditions. The first one, that √2=a/b, is the starting point for the proof so that's fine and the second one, that a and b are both integers, is used when asserting the evenness of a and b (because if you double something that isn't an integer the result might not be even), but the third condition, that a/b is in simplest terms (i.e. that a and b are co-prime) is as far as I can see NOT used in any step of the method until the final "contradiction" and so is in effect arbitrary. For example, suppose I said "let √4=a/b where a and b are both integers", but then imposed a third condition that a must be odd, I will get a contradiction because I can prove in a few lines that a is even.

So what is actually being proved here? If you drop the arbitrary third condition then it's NOT proving that √2 is irrational as such, but rather, because the doubling of a and b can carry on indefinitely, it's proving that √2 is the limit of some rational sequence involving powers of 2. So row me out in the boat with Hippasus if you must, but personally I'm quite happy that the limit of a rational sequence can be √2 as this was known even in antiquity (the so-called "Heron's method").

So, in the end, the ratio of even numbers is 4b-dden.

Can this guy stop saying 'ashhume' 6:06

actually, can't you just take root(2) = a/b, 2 = a^2/b^2, a^2 = 2 and b=1 (simplest terms) and therefore root(2)'s simplest form is just root(2)/1 and therefore it can't be a fraction?

Does math still have the same religious or spiritual significance it used to have then for people like the Pythagoreans?

It is rather easy to poke fun and ridicule some of the beliefs of ancient times and cultures, however we will do well to notice that even today fact does not always have and easy path.

Also one may question as to whether we are becoming more open minded or more prone towards group think?

1:45 Argh… One

square metreNOT one meter squared. The latter is an exact square with side 1m. The former is any area equal in size but can be any shape.Yes, when talking about

oneit's not that big of a deal but as soon as you are not usingone,it's important.Two metres squared is 4 square metres.

Maybe they persecuted Pythagores because he was a vegan. I find that the meat and dairy industry has been a corrupt and evil organization since the enslavement of mankind

what is 9+10?

I urinate where I want to urinate. Ain’t no star gonna tell me that.

I wish i had someone like you as my math teacher, would have made math a lot more intresting

Ok the sqrt(2) is irrational , then how can a ratio equal root(2) ?

Since you cant write an irrational number as a two number devided to each other?

So that's why when I blow up an A5 document to an A4 document on a photocopier I increase the size by 141%?

Chakju bicz

Pythagorasshole

I work in the printing industry and it is pretty common to round off at certain decimals.

A0 = 1 188mm × 840mm

A1 = 840mm x 594mm

A2 = 594mm × 420mm

A3 = 420mm × 297mm

A4 = 297mm × 210mm

A5 = 210mm × 148mm

A6 = 148mm × 105mm

A7 = 105mm × 74mm

A8 = 74mm × 52mm

A9 = 52mm x 37mm

You'll notice 148 isn't half of 297

148,50 is.

Like wise the short side of an A7 should be 74,25mm

It may seem petty, but calculating further on the practice of rounding off these sizes we'd end up with A20 being a square.

So while in formula the A-sizes will always be √2, in practice not so much.

Though the inner mathematician of me keeps the accuracy to the 2nd decimal after the comma, it is impossible to keep paper in exact ratios when cutting them in half, because it's paper.

In school we could get away with 22/7 as a very crude approximation.

The A series is used in most of the civilized world…

4:20 i never urinate towards the sun either, it's just disrespectful

we're here

we're irrational

get used to it

I'm watching this but I have a math exam tomorrow… so actually is not that bad

0:28 shouldn't it be phi/golden ratio?

Old school af baby

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