Legendre's actual appearance is also considered an unsolved math problem, the watercolor caricature by Julien-Léopold Boilly shown in the video is LITERALLY the only surviving portrait of the famous mathematician.
It is actually possible to "square the circle" employing a compass and straightedge, using the following procedure: 1) Mark a point on a circle's perimeter. 2) Rotate the circle 360 degrees (one full turn), tracing out a straight line segment. The resulting line segment is equal to the circumference of the original circle. (Imagine a can rolling on its side.) 3) Using the compass and straightedge, bisect the line segment into a half segment. 4) Bisect a half segment into a quarter segment. 5) Again using the compass and straightedge, construct a square with each of the sides equal to the quarter segment. The resulting square will have a perimeter equal to the original circle's. It won't be possible to state the exact length of the side of the square except as a ratio of Pi since Pi, which defines the circle's perimeter (circumference), is an irrational number. Nevertheless, the constructed square is a valid geometric representation of the squared circle. Neat, huh? Except for one problem: I cheated. You see, I didn't use just the two instruments, a compass and a straightedge, but also used a rotating marked circle. The rotating marked circle qualifies as a third "instrument", which is against the rules. Pi is not only an irrational number, but is also a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. Because the transcendence of Pi is involved, it would take an infinite number of steps to "square the circle" using only a compass and straightedge, making such a solution impossible. Sorry.
additionally the square having the same perimeter as the circle means it can't have the same area because circles don't have the big sharp pointy corners that add a lot of perimeter for not much area gain in fact, even if you could construct a line with length π with straightedge and compass, you need the square root of it, not just a quarter.
@@sergewind2208 You're right, the "squared circle" would not have the same area as the original circle. I should have realized that. Shows the hazard of making an assumption without verifying. 😮💨
@@alabamaal225all you have to do is “unroll the circle”, half it, and take the geometric mean of it and 1. Obviously still impossible because of “unrolling the circle”. But you can create a close approximation by forming an extremely close approximation of pi
When I first learned of the four color proof, I looked at it for myself. Right there in Illinois Journal of Mathematics vol. 21 are pages of hand drawn map diagrams. There is some cool stuff to be found in those bound volumes!
10:14 Some NATURAL* power greater than 2. The distinction is important between N+>2 and just "any number">2. I reread the proof yesterday and it's truly marvelous. Wiles' lifting theorem is exactly the missing puzzle piece number theorists had been searching for since the 1800s.
@kloklowewe4874 It's 12 squared as well as 12th on the Fibonacci Sequence. It showed up as the answer for the smallest fifth exponent thing as part of the Eulers thing. It's the 2^4×3^2 which I think is neat. How is it not cool?
in Fermat's theorem ∀n we use 2 terms - (x1)^2 + (x2)^2 = z^2 that if you use n terms for ∀ n, that is: (x[1])^n + (x[2])^n ... (x[n-1])^n + (x[n])^n = z^n tell the article where you can see it???
It's because a circle's constant is π/4 and a square is 1. (π/4)=/=1. That's also how we derive calculus, is through this same idea, of a curve proportioning area. You can multiply π/4 with any number, and get a relative circle constructed inside the square. Interestingly, the perimeter of the square and area, will always coincide with the circle's perimeter and area. They're just fundamentally different numbers, though. You could say the same for a hexagon constructed in a square, but again, you can't square the hexagon ether, as there will be an eccentricity ascribed to it, such as the square root of 2 is for a square. Sure you can probably get a number to fit in a square made from a hexagon, but like a square has an eccentricity of square root of two, a circle's is consistently π/4 on all sides--hence why intersecting chords theorem works. So it's a bit different, but a hexagon will have an eccentricity like π/4 or square root of two, too. How that would be used, I don't know.
I like this channel, but you’re really loose about names. For example in this video your pronunciation of Fermat or your misspelling and misnaming of Noam Elkies as “Noah Elkies”
8:12, yeah, but if for one value of B this ratio approaches 1 so it does for any other as lim x→∞ (x / (ln(x) - B_1)) / (x / (ln(x) - B_2)) = 1, to make any sense of "optimal value of B" you need to define some more strict way of comparing π(x) with x/(ln(x) + B)
Exactly! But it seems he copied this mistake from the Wikipedia article, which appears to state the same false deduction that π(x)/[x/(ln x - B)]→1 implies that B=lim(n→∞)[ln x-π(x)/x].
@@minirop of course, you are right. I knew it too. My first language is French. It’s just that I figured that actual correct pronunciation was too difficult for English speakers.😉
@isavenewspapers8890 Language usually isn’t that simple. Every language borrows words from other languages and sometimes you don’t even notice. Nonetheless it’s the same sound, regardless of wich language „fairy“ comes from.
Let's say the middle country is green. Then you can alternate red, yellow, red, yellow, red, yellow, etc. no matter how many countries there are. If there is an odd number of countries, then one country will need to be a fourth color.
![[#2024MAMA] BIGBANG (빅뱅) - 뱅뱅뱅 (BANG BANG BANG) + FANTASTIC BABY | Mnet 241123 방송](http://i.ytimg.com/vi/EQsYfiPR9uM/mqdefault.jpg)
Brilliant! Thanks 🖖
Glad you liked it!
Fermat be like: the proof is trivial and is left as an exercise for the reader
Legendre's actual appearance is also considered an unsolved math problem, the watercolor caricature by Julien-Léopold Boilly shown in the video is LITERALLY the only surviving portrait of the famous mathematician.
Time Traveler: Nice to meet you Mr. Fermat! I see that you are currently writing Fermat's Last Theorem
Fermat: My last what?
I like how you said "we know pi is transcendental because e is transcendental" without further explanation.
e is as I know easier to prove transcendental
Look into the Lindemann-Weierstrass theorem
What that photo for Legendre 😂
It's an unfinished caricature of him. It was meant to exaggerate his features in a comical way, as caricatures would.
@@orly4672 It's the only surviving image of the man, so it is still used.
@@renatofernandes1086 There is apparently another image too.
@@blindmoonbeaver1658 those were from some french politician with the same name
legrinch
It is actually possible to "square the circle" employing a compass and straightedge, using the following procedure:
1) Mark a point on a circle's perimeter.
2) Rotate the circle 360 degrees (one full turn), tracing out a straight line segment. The resulting line segment is equal to the circumference of the original circle. (Imagine a can rolling on its side.)
3) Using the compass and straightedge, bisect the line segment into a half segment.
4) Bisect a half segment into a quarter segment.
5) Again using the compass and straightedge, construct a square with each of the sides equal to the quarter segment.
The resulting square will have a perimeter equal to the original circle's. It won't be possible to state the exact length of the side of the square except as a ratio of Pi since Pi, which defines the circle's perimeter (circumference), is an irrational number. Nevertheless, the constructed square is a valid geometric representation of the squared circle.
Neat, huh? Except for one problem: I cheated. You see, I didn't use just the two instruments, a compass and a straightedge, but also used a rotating marked circle. The rotating marked circle qualifies as a third "instrument", which is against the rules.
Pi is not only an irrational number, but is also a transcendental number, meaning that it cannot be a solution of an equation involving only finite sums, products, powers, and integers. Because the transcendence of Pi is involved, it would take an infinite number of steps to "square the circle" using only a compass and straightedge, making such a solution impossible. Sorry.
I will be trying to square a circle for the rest of my life then
additionally the square having the same perimeter as the circle means it can't have the same area because circles don't have the big sharp pointy corners that add a lot of perimeter for not much area gain
in fact, even if you could construct a line with length π with straightedge and compass, you need the square root of it, not just a quarter.
@@sergewind2208 You're right, the "squared circle" would not have the same area as the original circle. I should have realized that. Shows the hazard of making an assumption without verifying. 😮💨
@@sergewind2208note that you can easily construct the square root of any given line segment by finding the geometric mean of it and a unit segment.
@@alabamaal225all you have to do is “unroll the circle”, half it, and take the geometric mean of it and 1.
Obviously still impossible because of “unrolling the circle”. But you can create a close approximation by forming an extremely close approximation of pi
When I first learned of the four color proof, I looked at it for myself. Right there in Illinois Journal of Mathematics vol. 21 are pages of hand drawn map diagrams. There is some cool stuff to be found in those bound volumes!
how does this guy not have millions of subs! this channel has crazy good quality
well, he has more subs than there are people interested in maths in the World, so there's that...
10:14 Some NATURAL* power greater than 2. The distinction is important between N+>2 and just "any number">2.
I reread the proof yesterday and it's truly marvelous. Wiles' lifting theorem is exactly the missing puzzle piece number theorists had been searching for since the 1800s.
Yeah, I read it over tea the other day while talking with colleagues. Quite ingenious. Quite.
02:00 sibelius opus 76 no 2 is the song
Thanks
144 is one of the coolest numbers in all the ways it tends to show up
No?
@kloklowewe4874 It's 12 squared as well as 12th on the Fibonacci Sequence. It showed up as the answer for the smallest fifth exponent thing as part of the Eulers thing. It's the 2^4×3^2 which I think is neat. How is it not cool?
I like 21
@monishrules6580 21 is also rad. I like to think of it as the bigger part of 121 (11^2).
@@lumbersnackenterprises numbers like pi or e show up in many cool ways, 144 does not, and the fact that it is a perfect square doesn’t change that.
in Fermat's theorem ∀n we use 2 terms - (x1)^2 + (x2)^2 = z^2
that if you use n terms for ∀ n, that is:
(x[1])^n + (x[2])^n ... (x[n-1])^n + (x[n])^n = z^n
tell the article where you can see it???
Great as usual.
It's because a circle's constant is π/4 and a square is 1. (π/4)=/=1. That's also how we derive calculus, is through this same idea, of a curve proportioning area. You can multiply π/4 with any number, and get a relative circle constructed inside the square. Interestingly, the perimeter of the square and area, will always coincide with the circle's perimeter and area. They're just fundamentally different numbers, though.
You could say the same for a hexagon constructed in a square, but again, you can't square the hexagon ether, as there will be an eccentricity ascribed to it, such as the square root of 2 is for a square. Sure you can probably get a number to fit in a square made from a hexagon, but like a square has an eccentricity of square root of two, a circle's is consistently π/4 on all sides--hence why intersecting chords theorem works. So it's a bit different, but a hexagon will have an eccentricity like π/4 or square root of two, too. How that would be used, I don't know.
Even a star trek episode refers to Fermat's last theorem not being solved... It's weird to see in a sci fi lol
A later episode in DS9 mentions the proof as a sort of retcon.
this is just serious huggbees
Omg yes!!! Someone finally said it
The name is _Noam_ Elkies not "Noah"
Lol I picked up on that too, that guy is too incredible to be misnamed like that
Fermat basically said CBF......
CBF like in geometry dash?
@@badpiggsI think
Click between frames?
C*ck ball frames
nah cant be f*cked
I like this channel, but you’re really loose about names. For example in this video your pronunciation of Fermat or your misspelling and misnaming of Noam Elkies as “Noah Elkies”
Amazing!
8:12, yeah, but if for one value of B this ratio approaches 1 so it does for any other as lim x→∞ (x / (ln(x) - B_1)) / (x / (ln(x) - B_2)) = 1, to make any sense of "optimal value of B" you need to define some more strict way of comparing π(x) with x/(ln(x) + B)
See equality at 8:47.
Exactly! But it seems he copied this mistake from the Wikipedia article, which appears to state the same false deduction that π(x)/[x/(ln x - B)]→1 implies that B=lim(n→∞)[ln x-π(x)/x].
Is this a re-upload?
In a way, isn't Euler's sum of power's conjecture, and Fermat's last theorem ... "sort of" the same?
Yes, that conjecture was intended as a direct extension of that theorem.
Euler's conjecture implies Fermat's last theorem. It's stronger. If it was proven true, that would have proven FLT, but it was proven to be false.
11:28 what is the name of the music?
Badinerie
5:35 - gotta ask: why that map in the background is in Polish :D?
Just a random video of a map. The specific choice of language doesn't seem to be relevant.
When is chapter 0 or 1
Just use infinite lines to get sqrt(PI).
okay and which one of these math problems is approximately billions of years old? eons?
Chopin La Valse du Petit Chien, makes me sad :/ hard to focus on the video
So wait if a squares area is π, does that mean its infinite ?
No, why would it mean that?
Fermat is pronounced « Fur-ma »
no, it's \fɛʁma\ (same vowel sound as in "fairy")
@@minirop of course, you are right. I knew it too. My first language is French. It’s just that I figured that actual correct pronunciation was too difficult for English speakers.😉
@@richardgratton7557 Isn't "fairy" an English word?
@isavenewspapers8890 Language usually isn’t that simple. Every language borrows words from other languages and sometimes you don’t even notice. Nonetheless it’s the same sound, regardless of wich language „fairy“ comes from.
@@Shooshpa-z2e What are you talking about? I wasn't asking what language "fairy" comes from.
Draw circular arms, eh?
What if a country is surrounded by more than 4 countries? How would 4 colors suffice?
Let's say the middle country is green. Then you can alternate red, yellow, red, yellow, red, yellow, etc. no matter how many countries there are. If there is an odd number of countries, then one country will need to be a fourth color.
ooo cool, i like learning about maths :P
I have an IQ of Legendre's Constant
all these are solved
nice
The way you keep mispronouncing fermat's name
Euler is not a "swiss" mathematician
Yes, he is.
He lived in Berlin for some time, but I would still say he was swiss in general.
@@newwaveinfantry8362 no he is not
Born in Basel. Which is, and was then, in Switzerland
you have a problem saying the nationality of Chebyshev for the same reason?
i know right
People mentioned in passing usually don’t get extra information. Like his name gt dropped *once* in this video.
❤
Are you an real person or an AI?
@@alexwarner3803 How much trolling until you get tired?
@faisalsheikh7846 real person
@@ThoughtThrill365Seems like somethings an AI would says…
video is called "unsolved problems" first problem is a solved problem... ?????? Clicked off
"The title contains a logical contradiction" lol