😮😮😮😮

+Zenytram Searom he said "Pie"

OMG!

All's hidden in numbers ;)

illuminati confirmed

Yea

No

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. (:

same system

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 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.

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

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

Aragorn Stellar by v.

Bruh my pure teacher is this excited about maths

Neat

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

@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!

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.

Beautiful!

So much kraft

Sharpies too...

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

were talking about two dimensions though lol

watch it from above :)

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.

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

+Mica Santos me

me

+Mica Santos We can also say pi bearly becomes 3.15

me 3

+Mica Santos me

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

이강민 Vantablack is brighter than mine.

ha ha :)

you almost made me choke laughing loll

and too close.

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

comment something else please

+Aditya Khanna You're right....

+Aditya Khanna creepy

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

thats funny

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

+burnsy96 I think you meant Fields medal.

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

burnsy96 I also live in Minnesota

Battle typhoon truuuuuuuuuuuuuuuuu

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

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

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

Cause he's brilliant. Duh!

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

Hopefully you had pi for dessert.

+The Changing Ways Meth Jokes.

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

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

levizna Either would be just as irrational.

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

+moonblink Cough, Calculus is more fun, cough

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

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

Tsavorite Prince a = c - b

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

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

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

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.

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.

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

@@alexeysaranchev6118 yaull’ses

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

@@puppergump4117 what's the correct way then?

@@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.

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

@@steffenjensen422 you can actually :)

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

+Enlightenment I did say. And you replied.

Glenn Beeson Do you know who I am?

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

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

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

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.

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

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

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...

Pi is burned in the prom

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

+McDanny420 Same way

Walking around a square is easy...

McDanny420 you got em there

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.

watching in 2016

+Desmond Dishwater watching in 2016.02716895

Still watching in 1996.

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

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

+( ͡° ͜ʖ ͡° )TheNoobyGamer 1.77245385090551...

Lastrevio There you go.

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".

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

+Clorox Bleach 3.2*

na because 3.14 does not round up

Clorox Bleach r/wooosh

π~3.2

π~~3.2

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

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

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)

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?

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.

As lenght of a segment too

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

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...

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

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

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.

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

NYEHEHEH...HEH

That's corier new. (I think)

you mean..THE GREAT PAPYRUS

That is Kraft paper

George Sorrell Thank you for that. :-)

Solved as in proven impossible.

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?

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

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

you can't use strings.

Rare Pokemon

why are you so shiny

When a reply gets more likes than the original comment

yup

+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)

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

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

Adarsh Singpuri ow yeah

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.

"Then you take a piece of paper and roll it up so that it exactly lines up with the circle. Cut of any excess. Unravel the paper. Find the length of the paper." None of these steps are allowed. You are only allowed to use a compass and unmarked straightedge.

And to be precise, the only allowed operations are to draw a line connecting two existing points, or a circle centered on one existing point and going through another, and then adding all points where the new line/circle intersects the existing lines and circles. (This assumes a "collapsing" compass. It has been shown that a "non-collapsing" compass, which allows taking a distance between two points and drawing a circle with that radius centered on the third point, doesn't allow any more constructions - any point that can be constructed with a non-collapsing compass can also be constructed with a collapsing compass.)

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.

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

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

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

+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. :)

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

+ʎɯɯıɾ ɔ haha...

+8070alejandro What's your preferred base then?

Lol