omg he said pi on 3:14, i can die now.

@aimeecortez5899

8 жыл бұрын

😮😮😮😮

@ellinaras4566

8 жыл бұрын

+Zenytram Searom he said "Pie"

@Danielkaas94

8 жыл бұрын

OMG!

@LightningJackFlash

8 жыл бұрын

All's hidden in numbers ;)

@johnplays9654

8 жыл бұрын

illuminati confirmed

soooo.... who's watching this after the 'pi nearly became 3.2' vid

@yiuyeungkan157

8 жыл бұрын

+Mica Santos me

@RizqieL

8 жыл бұрын

me

@kimberlychin1996

8 жыл бұрын

+Mica Santos We can also say pi bearly becomes 3.15

@AnteP-dx4my

8 жыл бұрын

me 3

@infinitegamer308

8 жыл бұрын

+Mica Santos me

But can you cube a sphere?

@adant9536

8 жыл бұрын

Yea

@MatteoBlooner

8 жыл бұрын

No

@zachmanifold

8 жыл бұрын

I gave it a try: This is for surface area, and I will do volume after. So, let's say 'Sa' = sphere area, and 'Ca' = cube area. Let's give the sphere a radius of five. Therefore, Sa = 4pi(5^2) = 314.16 units^2. Now we have Ca which is an unknown. The formula for the area of a cube is 6a^2, so to get rid of the 6, I divided the area of Sa by six, which gives us (314.16 / 6) = 52.36. Now we're left with a^2 = 52.36, so I took the square root: sqrt(52.36) = 7.236021. So a = 7.236021, now let's plug it into the formula for the surface area of a cube: Ca = 6(7.236021)^2 = ~314.16. Seems like we got surface area, now let's do volume: A sphere with a radius of five (just like the sphere above) = (4/3)pi(5^3) = 523.6 units^3. The formula for the volume of a cube is a^3. We already solved for a when a sphere has a radius of five, so let's plug it in: (7.236021)^3 = 378.88 units^3. The cube appears to have a lesser volume than the sphere. ((523.6 / 378.88) * 100) - 100 = 38.2%. The sphere's volume is about 38.2% larger than the cube. Thanks for taking the time to read, I hope my maths is all correct. (:

@unicockboy1666

6 жыл бұрын

same system

@unicockboy1666

6 жыл бұрын

Figgy Winks Clear NO: you multiply the radius by an infinite number, so that you cant take the 3rd root (or any root in fact) out of it...

I love how obviously excited you get about math. That more teachers would have such zeal.

@thanatosdaughter6298

8 жыл бұрын

I completely agree! He's so obviously passionate and it's great. If my teachers were like this, I'm pretty sure I would have a lot more fun in my classes.

@Schobbish

7 жыл бұрын

The thing is that I probably learned more from this channel than my math teachers. (Sorry math teacher...)

@seanp4644

7 жыл бұрын

+Nathan Adam (SchobbishBot3000) don't apologize. These guys do it better.

@supersohig3671

7 жыл бұрын

Aragorn Stellar by v.

@Tom-vu1wr

3 жыл бұрын

Bruh my pure teacher is this excited about maths

make a circle out of playdoh, then mold it into the shape of a square, wheres my nobel prize?

@michaelbauers8800

8 жыл бұрын

You would have to keep the playdough perfectly flat and the same height it originally was.

@aiden359

8 жыл бұрын

were talking about two dimensions though lol

@ingolfura.4327

8 жыл бұрын

watch it from above :)

@jimbobago

7 жыл бұрын

a) There's no Nobel Prize for Mathematics b) No one's saying you can't solve the problem with Play-Doh. It's only impossible under the rule that you have to do it with nothing but a compass and unmarked straightedge.

@Edgard422

7 жыл бұрын

That's a compressible material, no nobel prize for you.

His skin is brighter than my future.

@ObsidianShadowHawk

8 жыл бұрын

+stripeysoup Making me laugh at 3am... Thank you, sir!

@reizayin

7 жыл бұрын

이강민 Vantablack is brighter than mine.

@vijayshejal4322

7 жыл бұрын

ha ha :)

@onyxgod777

6 жыл бұрын

you almost made me choke laughing loll

@clayz1

6 жыл бұрын

and too close.

*Greeks:* Straight edge and compass *Numberphile:* Straight edge, Ccompass and loads of brown paper.

@Mike-739

3 жыл бұрын

So much kraft

@mohammadumair3108

3 жыл бұрын

Sharpies too...

In case anyone is wondering about the square root thing at 2:15, it's pretty simple. The ratio between the dotted line and 1 has to be the same as the ratio between a and the dotted line, because if you draw lines from the ends of the diameter to the top of the dotted line, the resultant triangles have the same angles. It would be a lot better if I could draw this out, but hopefully you can visualize it. In other words, call x the length of the dotted line, and you have x/1 = x = a/x. Therefore, a = x^2, so x = sqrt(a).

@philipk4475

4 жыл бұрын

Neat

@idzudinsaffuan9095

3 жыл бұрын

@U.S. Paper Games exactly. the ratio couldnt be the same

@johnnye87

3 жыл бұрын

@U.S. Paper Games Maybe your description is unclear but it doesn't sound like you're doing what the video demonstrated. You need a semicircle of *diameter* A+1, with a line segmenting it 1 unit from the perimeter. If our radius is 15, then A (the number we're going to find the sqrt of) is 29. So our dotted line is 14 units from the centre, and forms a right angled triangle with the radius such that its height is the sqrt of (15 squared minus 14 squared), ie root (225-196), ie root 29. Which shows you what's happening in algebraic terms: the length of A (diameter minus 1) is 2r-1, and the Pythagorean formula gives you the sqrt of (r sq minus r-1 sq)... which simplifies to the sqrt of 2r-1. Neat!

@E1craZ4life

2 жыл бұрын

If you draw a rectangle and then draw diagonals connecting opposite vertices, the diagonals would bisect each other. So drawing a circle with a center at the intersection point between the diagonals would pass through all four vertices of the rectangle if it passes through one of them. What that means is that any triangle with points on a circle is a right triangle if the hypotenuse is the same length as the circle's diameter. If a line is drawn perpendicular to the hypotenuse passing through the point opposite the hypotenuse, then this will produce two smaller right triangles. Since the sum of a triangle's angles has to be 180 degrees, the smaller triangles will be similar since the original right angle was split into two smaller angles. By that logic, the smaller leg of the smallest triangle would have to be scaled up by a factor of the longer leg to match the size of the other triangle. And that in turn, means the longer leg of the larger triangle has a length equal to the shared leg's length squared.

@franciscohamlin7544

2 жыл бұрын

Beautiful!

Why is he so shiny?

@galek75

9 жыл бұрын

Battle typhoon truuuuuuuuuuuuuuuuu

@frtard

9 жыл бұрын

Battle typhoon Too much maths. It's coming out his pores.

@Toimi

9 жыл бұрын

Battle typhoon He's a robot. His skin is actually plastic.

@nourse

9 жыл бұрын

Battle typhoon He's shiny and chrome to go to valhalla.

@castleblack6941

8 жыл бұрын

Cause he's brilliant. Duh!

Guys I found the solution to this so called 'unsolvable problem' and I will patent it so you have to pay me when you math it out except for my home state Minnesota as a gift to them.

@fullyverified7491

8 жыл бұрын

thats funny

@burnsy96

7 жыл бұрын

Tsavorite Prince Yes, I'll get the Nobel prize for this one

@General12th

7 жыл бұрын

+burnsy96 I think you meant Fields medal.

@LivingChords

7 жыл бұрын

no i'm pretty sure he meant the nobel prize.

@Carter040404

7 жыл бұрын

burnsy96 I also live in Minnesota

At time 3:14 he said "Pi"

@njood96

8 жыл бұрын

Aditya Khanna and now your comment likes are 314 XD i want to like it but i don't want to ruin it XD

@zashtozaboga

8 жыл бұрын

comment something else please

@thefremddingeguy6058

8 жыл бұрын

+Aditya Khanna You're right....

@rongliu3339

8 жыл бұрын

+Aditya Khanna creepy

@coopergates9680

8 жыл бұрын

+Стилиян Петров I think the Zeno's paradox video doesn't say how you could really "make" a square with side Sqrt(pi).

you cannot theoretically square a circle, but realistically you can. in realist terms we are left with approximations determining the effectiveness of theorems in geometry, physics, etc. if you can find me a perfect circle in real life that has exactly an area of x^2xpi, and you can prove it to any digit within pi with no room for error, i'd eat my house.

@coopergates9680

8 жыл бұрын

+Daniel Williams (Invents arbitrary unit such that x = 1)

I once ingested an e. It was truly a transcendental experience. ‪#‎MathJokes‬

@SpaceGuru5

8 жыл бұрын

Hopefully you had pi for dessert.

@Intel1502

8 жыл бұрын

+The Changing Ways Meth Jokes.

@losthor1zon

8 жыл бұрын

+The Changing Ways - Hope it didn't require a transcendentist.

@qclod

8 жыл бұрын

+SpaceGuru5 I can eat a whole pi, but a tau is too much to handle.

@SpaceGuru5

8 жыл бұрын

levizna Either would be just as irrational.

I love Dr James Grim's enthusiasm when he tries to explain such not so easy math problems. I wish I had such a math teacher. Or all my teachers. Fantastic!!! Thank you.

10 years later and I still come back to these videos videos 😅

Algebra rocks. I've been explaining that to people since high school. Algebra is there to make sense of everything. Algebra is like the ABC's of math.

@TehKorwinMikke

8 жыл бұрын

+moonblink Algebra is THE alphabet, words, and sentences of math, yo.

@carbon13

8 жыл бұрын

+moonblink Cough, Calculus is more fun, cough

@carbon13

8 жыл бұрын

***** But the fundamentals of Calculus differentiate from every other form of Algebra.

@carbon13

8 жыл бұрын

***** Really depends on what you're doing with your programs.

@moonblink

7 жыл бұрын

Tsavorite Prince a = c - b

I really wish I had had y'alls videos when I was a kid. I think I would've liked math A LOT more.

@alexeysaranchev6118

4 жыл бұрын

What sort of videos could've made you love the English language enough not to use "y'alls"?

@nickwilson3499

3 жыл бұрын

@@alexeysaranchev6118 yaull’ses

@puppergump4117

2 жыл бұрын

@@alexeysaranchev6118 It's about as improper as your use of "could've". Sieg grammar I guess.

@alexeysaranchev6118

2 жыл бұрын

@@puppergump4117 what's the correct way then?

@puppergump4117

2 жыл бұрын

@@alexeysaranchev6118 It's only correct if you stick to one standard. Either accept contractions or don't. Since contractions are accepted by the vast majority, with the exception of some college teachers, the use of both "y'alls" and "could've" are grammatically correct. Of course, not in the technical sense. However, if half of our country accepts a form of a word, who cares if some college's dictionary accepts it? Language is meant to express meaning, not to be restricted by redundant rules.

Dr Grime sure is a bright man, no pun intended!

It is possible to use materials that the Greeks had at their disposal to "square the circle": Draw circle, radius 1 (area=π) Outline circumference with string, straighten out the string, then draw line (this has a length of 2π) Divide length by 2, use triangle scaling method Use the square root finding method thing with the semicircle (to get √π) Side for square has been found Of course, there will be some error due to the elasticity of the string and the human impossibility of perfectly measuring where the string coincides with itself after one rotation among other factors, but theoretically and statistically speaking it is possible

@kevinoduor9841

7 жыл бұрын

use a ruler and a compass only, that's the rule.

@KnakuanaRka

6 жыл бұрын

The Greek problem only permitted compass and straightedge; there is no way to emulate your “straighten out the string” bit under these rules.

@hanniffydinn6019

6 жыл бұрын

Yeah, simple really, it's called string theory !!!

@pbierre

5 жыл бұрын

You're allowed to use the compass as a caliper to copy distances, right? So break up an arc length into a series of piecewise line segments, and copy them out to a straight line length. If you solve for the half-width of the square , sqrt(pi/4), you only need to "linearize" 1/8th of the unit circle arc.

@KnakuanaRka

5 жыл бұрын

Pierre Bierre It wouldn’t be possible to exactly replicate the length of the arc unless you used an infinite number of line segments, which is not allowed, as the construction must be finite.

I love this channel and return to it often. Not only fascinating and educational, but the sheer excitement and clarity by Numberphile is a joy to behold!

I really love how passionate he is about mathematics :D it's amazing.

lol I love this guy. Great smile and he absolutely enjoys his field.

Thank you for not having distracting background music, like so many others! Like given.

The fact that we can't just change our units to solve this also points to something transcendental

Awesome presentation! Thank you! I hated straight edge and compass problems back in junior high (esp. the "is it possible" type, which are way harder than the "construct..." type). I always wondered what the point was. I wish this video had been my introduction to straight edge and compass.

This channel made me like maths and now I'm an educator sharing problem solvings based on calculations ❤️

4 years later still watching, again. Numberphile

Im so hypnotized by him, thats the stunning thing in these Numberphile clips, these people have a passion with their theme, its so fun to watch.

Wish I saw enough videos of numberphile before finishing high school. I would have been more interested in maths, not that I wasn't interested at all.

What about circling the square?

@olli343

8 жыл бұрын

+McDanny420 If you can find a circle with the area of a square, you have square with the area of a circle, sooooo...?

@cclupu

8 жыл бұрын

+McDanny420 Same way

@seanp4644

7 жыл бұрын

Walking around a square is easy...

@chlover5853

6 жыл бұрын

McDanny420 you got em there

@Theo_Caro

5 жыл бұрын

We are given a square with side length "s." We need to construct a segment with length "r" so that s^2=pi*r^2. Since s is a constructible number, pi*r^2 is constructible. However, we know that pi is transcendental and not constructible so that pi*r^2=s^2 is not constructible, a contradiction. Thus, we cannot construct a circle with an area equal to a given square. Squaring the circle and circling the square are logically equivalent in fact. "Squaring" was a word for what we know call integration. So the problem is really one in just being able to talk about the area of circles in terms of how we normally measure area (i.e. with rectangles). The problem fundamentally is about the nature of pi. And the solution is ehm... really cool.

You people are wonderful wonderful people. I've never been great at math but it's really fun to watch your videos and enjoy it without worrying about skill

I love James' skill at explanation but can I just say how CUTE he is too?! :D

I'm not really into math, but so far I'm enjoying these videos, Good job!

I wonder what goes through your head when you solve a problem like this

Awesome videos, man, I watch a few of them every day and re-watch them every few days. Fantastic!

I wish u were 1 of my teachers in school. I hated math class but seeing someone who not only actually enjoys it but is also passionate about it brings a lot of excitement to the subject.

This is friends talking about cool stuff! Loving it!

How does calculating Pi with a calculator work? I did a simple experiment once, I typed in 3.14 instead of using Pi on the calculator, then afterwards I did the same formula again, this time using Pi, and as some of you probably already have guessed, the numbers where quite different. My question is then if the button for Pi on my calculator, is defined with a very long row of numbers, or if there's another method used in the calculator's programming to define Pi?

@Aerxis

7 жыл бұрын

Pi digits can be calculated using taylor series, among other methods, but your calculator is only using a fixed set of digits (10 or 12), most likely.

@Aerxis

6 жыл бұрын

Slimzie Maygen Not all of what you said is true, and I fail to see why is it relevant in connection to my reply.

@drearyplane8259

6 жыл бұрын

Twinrehz My calculator has a verify mode, and, using this, I found it uses 13 digits of pi.

@unicockboy1666

6 жыл бұрын

Its using a lot of numbers (depending on your calculator), but not quite pi. It only comes so close to it, that for us and our practical universe, it doesn't matter anymore. In fact you cant even form a perfect cirle of sphere in real life...

@pedrosaenzsantamaria2358

6 жыл бұрын

Pi is burned in the prom

Quite happy to be strung along by these two!

He looks so excited at 4:35 talking about transcendental numbers. It's adorable.

Algebra is brilliant. I knew it!

@gfetco

8 жыл бұрын

+Glenn Beeson (BeesonatotX) You don't say.

@DudeGlenn

8 жыл бұрын

+Enlightenment I did say. And you replied.

@gfetco

8 жыл бұрын

Glenn Beeson Do you know who I am?

@DudeGlenn

8 жыл бұрын

+Enlightenment You know that I don't hence the question. I assume this is going some where correct?

@gfetco

8 жыл бұрын

Glenn Beeson I am Ronnie Pickering! Don't you forget! :D

Squaring the circle? If you think that's difficult, try Cubing the Sphere! I've been trying to do that for the last 141 years!

Numberphile still going strong during the corona-lockdown! Fabulous!

This isn't how I've heard of "squaring the circle" I'm thinking of something different I guess but I thought it was a (possibly equivalent) problem of dicing up a circle in such a way that you could construct a square from its pieces. And I think this was solved relatively recently, but using some not very satisfying feeling rules.

@steffenjensen422

4 жыл бұрын

No, the problem your describing is trivial. Just look at the curved parts, you're not gonna get rid of them

@nikhilnagaria2672

2 жыл бұрын

@@steffenjensen422 you can actually :)

I have never been so interested in math in my whole life.

Still watching in 2015

@samkollmeier753

8 жыл бұрын

watching in 2016

@AoSCow

8 жыл бұрын

+Desmond Dishwater watching in 2016.02716895

@Alliloux

8 жыл бұрын

Still watching in 1996.

@AoSCow

8 жыл бұрын

***** The video was made in 2013 March. So it's closer to pi years.

You are amazing. I feel that I could love maths with you enthusiastic presentation. Thank you!

That you speak about maths with such enthusiasm it makes me so happy.

In case you didn't get it: √2 is an algebraic number because is is the square root of a rational number. Although there is an n where √n = π, there would have to be another number (let's call it 'm') where √m = n, and (let's call the next one 'p') where √p = m, and so on to infinity, That's why π is not an algebraic number.

@steffenjensen422

4 жыл бұрын

You left out the crucial point that none of those numbers are rational

2:32 - mind blown.

I absolutely love this channel its marvelous

Use the last way to construct a number. Draw a line sized pi, add 1, make a circle with pi + 1 and the height will be sqrt(pi). Get this dimension with a compass and draw the square.

I wish I had math teachers that were excited about math and could rub it off on their students. Well, I did have a few, and their classes were the ones I passed. But other teachers I had, especially my college teachers... Well, I didn't take anything away from them. Now I'm going on a self teaching spree with math.

At 2:26, why is the length equal to √(a)?

@BrickfilmMan

7 жыл бұрын

Thanks for your reply, but I still don't quite understand. What does that have to do with the length?

@jeymsie2474

7 жыл бұрын

This is also new for me so I tried searching for proof but sadly there was'nt any in the net so I made my own proof. Bear with me please. From that semi-circle, make a line from the upper part of the line measuring √(a) and connect it to the center to make a radius. So now we have a right triangle and we can make use of Pythagorean's theorem. The diameter measures (a+1) so we can say that the radius is (a+1)/2, so... HYPOTHENUSE = (a+1)/2 LEG 1 = √(a) Now, leg 2 is just the radius minus 1 right? So that means, LEG 2 = ((a+1)/2) - 1 OR (a-1)/2 Now, using pythagorean's theorem, √(a)^2 + ((a-1)/2)^2 = ((a+1)/2)^2 a + (a^2 - 2a + 1)/4 = (a^2 + 2a + 1)/4 4a + a^2 - 2a + 1 = a^2 + 2a + 1 4a - 2a = 2a 2a = 2a So that's it, hooray or something

@Sonny_McMacsson

7 жыл бұрын

If the arc's diameter (a+1) is labeled A_B, put a point C where a and 1 meet then move up perpendicular to A_B until it touches the arc at D. Triangle ABD is a right triangle therefore triangles ACD and BCD are similar. The relationship exists: B_C / C_D = C_D / A_C (1) The lengths are: B_C = 1 (2) A_C = a C_D = b Substitute lengths (2) into (1) to get: b/a = 1/b Therefore: b^2 = a b = √(a)

@BrickfilmMan

7 жыл бұрын

embustero71 Thank you very much for your proof! :D It works very well, and I understand it! Just one quick question, why is the value of angle ADB a right angle?

@Sonny_McMacsson

7 жыл бұрын

Brickfilm Man Draw two intersecting diameters in a circle (they'll cross at the center of course). Take care to notice that the outer hull of the four points where the diameters meet the circle just happen to make a rectangle with the diameter segments being its diagonals.

You guys are freaking great. Thank you very much!!!

i lovehate this channel so much. its so interesting that i end up clicking video after video in my recommended late into the night and i cant sleep because i need to ABSORB ALL THE KNOWLEDGE IN THE UNIVERSE

How can one derive the area of a circle? Imagine a circle is superimposed in a square such that the r of the circle is equal to half the side of the square. The area of the square is known as s^2. Suppose one didn't know the formula for the area of a circle. How would he/she derive it from this information?

04:22 I thought Algebraic numbers are numbers which solve "rational coefficient equations" - not necessarily "constructable numbers". Like ³√2.

James, love you!

I love this channel!

You can only ever approximate the area of a circle.

@cclupu

8 жыл бұрын

As lenght of a segment too

@harinandanrnair6768

7 жыл бұрын

Fleegsta no and yes ....actually Area of a circle is exactly pi times r^2, but as u said it can only be approximated because pi can only be approximated

@cclupu

7 жыл бұрын

For Harinadan Nair : But if you put r=Pi the area becomes r^3. Isn't so weird if you use the fact in physics...

@simonruszczak5563

6 жыл бұрын

Because a polygon of infinite sides can't really exist.

While trying the squaring of the circle, Is it allowed to use a thin string or twine? I mean: If i draw a circle with radius 1, i can messure the lenght of the semi circle with the twine. Now i have the lenght pi and can draw a line of this lenght + 1. Then i can draw the semi circle over this line and can messure the square root of pi like the square root of a in the video. And now i have the length to draw the sides of the square. Or am i making any mistake here?

@raykent3211

8 жыл бұрын

I was thinking along similar lines in the video about an attempt to legislate that pi = 3.2. Here, the prof emphasises that they were playing by certain rules. You've stepped outside the rules that are considered pure mathematics. But I bet ancient greek engineers didn't rely entirely on the mathematicians. Archimedes invented a simple machine (trammel) which draws ellipses. If it could be made perfectly, they'd be perfect ellipses (proven by mathematicians). But it's less "pure" than just straight-edge and compasses. Who makes the rules?

@siekensou77

8 жыл бұрын

i think they would have access to string or twine..

One thing that I would like to point out is that there are ways of solving this problem as well as the other two famous impossible problems of Euclidean Geometry. The three problems are 1)Squaring the Circle, 2)Doubling the Cube, and 3)Trisecting an Angle. However, it requires us to move away from Euclid's axioms. 1) & 3) can be solved using the Spiral of Archimedes and 2) can be solved using parabolas. Perhaps Numberphile can make a video about those constructions in the future.

You always have that Rubik’s cube. Can you solve it in a video sometime?

So, a circle with radius 1 is just a pie with π area

@Marcelo-yp9uz

4 жыл бұрын

@Fester Blats No, a circle with a diameter of 1 has an CIRCUMFERENCE of pi

@egs_mythicgamer4013

3 жыл бұрын

Anifco67 No they’re right the area formula is pi times r^2 so if r is 1 then the area would just be pi.

Algebra is a tool of convenience. Makes sense to me. A lot of what the arabs did was taking greek texts that came from all over the place and just consolidate it into something more interpretable.

his passion is infectious..,

Thanks a lot for the wonderful videos over the years. Just to highlight that the fact that you can approximate the side of a square that has the same area with a given circle using algebra, doesn't mean that it can actually be done. Since you can only approximate it and not really find it (pi is transcendental), it doesn't exist, no matter the intermediate tools you are using, computers or otherwise. The only tool we have in any case is our mind. Thanks again!

π=3.2

@Molly_Bloom_

7 жыл бұрын

+Clorox Bleach 3.2*

@ryanbright2696

6 жыл бұрын

na because 3.14 does not round up

@DerUbermonke

5 жыл бұрын

Clorox Bleach r/wooosh

@006bartdiebrak7

4 жыл бұрын

π~3.2

@006bartdiebrak7

4 жыл бұрын

π~~3.2

You guys need a board or something. Papyrus has been used too much...

@AiZeno

8 жыл бұрын

+Oh Kazi but those are recycled paper aren't it? (not papyrus, but the paper used in their videos)

@askingstuff

8 жыл бұрын

NYEHEHEH...HEH

@hetakusoda2977

8 жыл бұрын

That's corier new. (I think)

@pe3akpe3et99

4 жыл бұрын

you mean..THE GREAT PAPYRUS

@Mike-739

3 жыл бұрын

That is Kraft paper

Love these vids!

Archimedes merely found one of a long series of approximations. As mentioned in the video, Ramanujan found a very close one too. What happened in 1882 was that it was finally proven that the circle in fact CANNOT be squared using just a straightedge and a compass. When they say the problem was "solved", this is what they mean.

what about strings? you cant put a string around a circle of radius 1, and then divide by 2? this would be pi with no doubt

@ilyatoporgilka

4 жыл бұрын

You would not be able to calculate it further after millimeters,microns,atoms,etc.

@harryw4802

3 жыл бұрын

you can't use strings.

Can someone explain why the sqrt(a) part of the semi circle is sqrt(a)? or just explain the steps for finding the measurements of the semi circle? thanks!

@Titurel

8 жыл бұрын

+Angel Urbina Draw a triangle by connecting the ends of the diameter to where the line sqrt(a) (call this line "h") meets the circumference. This larger triangle is a right triangle. The two smaller triangles are also right triangles. All are Similar (check by adding up angles) in two smaller triangles ratio of a/h is equal to h/1. so h^2 equals a*1 so h equals sqrt (a*1)

@fifafutbeast

8 жыл бұрын

+Titurel ohhhhhh... that makes sense. thanks!

This channel is severely underrated

I've watched this video for years now and I don't understand one thing. Until last week, I couldn't find any other reference of geometric constructions of arithmetic. I don't understand how multiplication/division works. Do I use an arbitrary angle? What about the unlabeled sides to the right? Is it an isosceles right triangle? Thanks to the person who clears this up to me.

Step 1: Make a circle with the radius 1 Step 2: Cut a wire the same size as the circle's circunference Step 3: Wire equals Pi Step 4: Make a line the size of the wire, add the 1 which we used for the radius Step 5: Take the square root of pi Step 6: Cut a wire of that size Step 7: Use wire to draw a square with the sides equal to the square root of pi Done.

@fiona9891

8 жыл бұрын

+( ͡° ͜ʖ ͡° )TheNoobyGamer *Looks at comments* Oh, this has been said before? Anyways, can someone figure out sqrt(π) ?

@Lastrevio

8 жыл бұрын

+( ͡° ͜ʖ ͡° )TheNoobyGamer 1.77245385090551...

@fiona9891

8 жыл бұрын

Lastrevio There you go.

@enderman6777

7 жыл бұрын

but the wire's length would not be exactly equal because of physical limitations (atoms; material decay; acuracy and all that). You'd get, for the length of the square, and approximation of the length "root of pi".

@gilbertonogueira3481

6 жыл бұрын

Assuming it would possibly work, the lenght of the wire would equal 2Pi, not Pi.

Easily! You can make a square with holes in a fractal pattern to get it, that might not count as a square though, so...

James Grime...the man who made me love math

doggonit numberphile. I'm trying to do math homework; I take a study break, and I decide to watch a silly 4 minute video. Instead of being 5 minutes you string me along for a half hour. errrggg

Why is he so shiny xD

@TigerXeN

7 жыл бұрын

Rare Pokemon

@ryanlira7194

6 жыл бұрын

why are you so shiny

@Ghost____Rider

6 жыл бұрын

When a reply gets more likes than the original comment

Numberphile At 0:13 James says that squaring the circle was solved in 1882. Please show us how...

@BillySugger1965

9 жыл бұрын

George Sorrell Thank you for that. :-)

@Scy

9 жыл бұрын

Solved as in proven impossible.

this is the best channel.! Video every 60 squared second.

Brilliant Video.

So the greeks didnt have numbers or algebra but they did have square roots?!

@harryw4802

3 жыл бұрын

yup

i don't understand how you get the root 'a' part by adding 1?

@polpat

6 жыл бұрын

Between the diameter and any point on the circle you get a straight triangle. When you add the vertical line he added you get 3 similar triangles. Similar means their ratios are the same. write down the equality between the ratios in the triangles having this vertical line in common. As you will see it shows that the unknown length squared is a.

Hes my favorite numberphile.

hes the only guy that makes me entertained

That unsolved rubik's cube was driving me crazy. Anyone else?

@mr.j_krr_80

6 жыл бұрын

Adarsh Singpuri ow yeah

@ilyatoporgilka

4 жыл бұрын

Search "Radio cube 3".It is a shape mod of another difficult puzzle "Eitan's star".Basically,an icosahedral variant of a Rubik's cube. In my channel you can watch hundreds of videos about that kind of puzzles.Go and do so.

If we had no algebra there would be no cities. There probably wouldn't be any computers either, but that's all I'm saying.

@gavinwightman4038

7 жыл бұрын

Andrew S We wouldn't know the distance of roads with curves.

@unicockboy1666

6 жыл бұрын

Dr Scrubbington There is an explanation below a comment about the same question

every time I watch a numberphile video, I wish I had dedicated more of my time at high school to appreciating maths.

He said Pie, on 3:14, on March 14, I am complete now, thank you Numberphile for activating the heehoo neurons in my brain.

Take a tube with a radius of 0.5. Wrap a sheet of paper around it. Draw a line around the perimeter. Unfold the paper. You now have a line with a length of PI. Done. You just need to use warped space. Next problem?

@BetaDude40

5 жыл бұрын

This problem only works in Euclidean space, you can't use a third dimension.

Just because you don't know all the digits of pi doesn't mean that a square cannot have an area of exactly pi.

@angelmendez-rivera351

5 жыл бұрын

Starscream That's not what he claimed. Did you watch the video?

Can’t you draw a circle with radius 1, use a string to measure circumference, hold the string to draw a line of length pi, and do the circle thing to draw a line of length root pi and then make it a square?

@MikeRosoftJH

4 жыл бұрын

Maybe, if you can have the string exactly follow the circle. But this is not what the theorem is about. It's not about what lengths can be constructed using some physical device; it's about what lengths can be constructed using a finite sequence of precisely defined operations: start with two arbitrary points (we'll consider the distance between them to be equal to 1); then repeat the following operations: Add a line connecting two of the existing points, or add a circle centered on one point and going through another; then add all points where the new line/circle intersects the existing lines or circles. (It can be proven that lengths which can be constructed by a finite sequence of previously described operations are precisely the numbers which can be expressed as a formula with integer coefficients using addition, subtraction, multiplication, division, and square roots.)

Numberfile has 3.14 million subscribers at this exact moment

6:22 you forgot .org

@nzmfpv

4 жыл бұрын

Lol

Here something that has always bugged me, maybe you numberphiles can help. the sum of the product of 9x anything = 9. eg 9x1 =9. 9x2 =18 the sum of the product = 9 (1+8=9) This works for 9 x anything. Why

@AlsteinLe

8 жыл бұрын

it's cause it's always missing 1 from 10. u can think of it being +1 instead of +9/-1. so if it counting +1 for each number u got. it's the same as that number . ex 5=+5

@bjornsahlin

8 жыл бұрын

+Paul Dogon Look up modulo calculation and/or the proof of why a number is divisible with 9 if the digit sum of that number is divisible by 9. :)

@user-zh3sn6fo5o

8 жыл бұрын

+AlsteinLe Can i sue u? U just made me brain wrinkle.

@AlsteinLe

8 жыл бұрын

+ʎɯɯıɾ ɔ haha...

@coopergates9680

8 жыл бұрын

+8070alejandro What's your preferred base then?

Make a right-angled triangle with vertices at the centre of the semicircle, and the top and bottom of that root (a) line.

It’s brilliant. It’s not the ad.