The ratio between a League of Legends player’s ego to their elo is called the “Feeder’s Constant” and is approximated to infinity. It is represented by this equation and symbol: Ego/Elo = ∞. Curiously, the difference between both variables Ego and Elo, commonly referred to as the “Inter’s Gap” is also equal to infinity: Ego - Elo = ∞. This paradoxically converging phenomenon is known as the “Bronze-Iron Effect”.
Theorem: Let G=(X,Y) be an ranked game, where X (also knows as allied team) and Y (also knows as enemy team) are sets with cardinality 5. (i) If X contains a Yasuo player then its death count sequence approachs to Infinity. (ii) If Y contains a Yasuo player then its kill count sequence approachs to infinity. Proof: We will prove only (i), (ii) is left as an exercise. We know that G is a ranked game and X contains a Yasuo main so by Incarryable theorem (Leonard Faker, 1953) we have that the kill count sequence follows the formula K = 2^t, its trivial proof that diverges to Infinity. Q.E.D
You can also get the value this way : If their IQ is nearing 0 then their ego is usually represented as such : Ego = Limit(x=> 0+) 1/x ~ infinity 0+ being any value that approach 0 from right side
In effect, yes. The magic is the applications that can arise. The amount of applications euler's number opened up were amazing, especially due to it being originally studied as an oddity in old Logarithm tables.
@mr.duckie._. "the difference between science and messing around is writing it down" the cool thing about math is that you (usually) dont need super expensive shit to mess around
Mathematics is a hobby. I believe much of these constants emerged because mathematicians experimented with numbers to see what kind of equations they are going to get
2 things from me to you: Correct! And this is called: “Number theory” which explores the property of numbers, variables, constants, and irrational numbers that have unique properties. Another thing is that most of these are from either accidents or coincidence and then eventually their work gets recognized and published to the public + recognition.
There are constants literally named after materials followed by 'ratio'. They're literally obviously Messing around and finding out Lets create the wooden ratio
Nah, usually people do at least something to get their name on a constant, for instance Brun's constant (7:32) is named after Viggo Brun because he invented a new proof method to prove it is finite
most of these constants have mathematical usefulness in one proof or the other and were not made up for sheer fun even if it appears that way in this video
1:51: The Magic Angle is exactly half the tetrahedron angle of 109,47°, which is arccos(-1/3) or 2 arctan(√2). Which means that the Magic Angle is exactly arctan(√2).
What is allways amazing to me, is how many of those seemingly random "useless" constants can be found in natural sciences (next to the natural constants), makeing their discovery and exploration of their behaviour exceedingly relevant.
One of the constants that I really like and I think you missed is, historically, a number that is described quite a bit after pi is described The humanity's first attempt to extend their number system It's the constant zero! // Also regarding Dottie's number, it is probably also one of the constant that us nerd's accidentally stumble on while we were a child: noticing that pressing cos repeatedly on a calculator makes the number converge.
Love the video, great animations. But I have a question.... Is anything past like 22 actually useful in maths? Sounds like I could come up with a random sequence, then calculate a constant.. now it's useless... I have quite some research ahead of me.
This question actually deserves a thoughtful reply. This sentiment is something that students who are farther along in their studies, specifically in pure math, need to make peace with as it's not a given what 'useful' math is. In short, these feel like a vague jumble of facts, especially when presented in this rapid fire format - it's hard to see the beautiful applications of them, sort of like reading the dictionary, you don't get all the beautiful synthesis of language from that!
It depends on what you mean by "useful", but some of these are meaningful. Apéry's Constant, 26, is zeta(3). The zeta function is a very famous function used in number theory, and studying it helps us understand the distribution of prime numbers. Historically, a problem known as the Basel problem was basically "compute zeta(2)". Euler solved it, and even computed zeta(2k) for any positive integer k. It turns out all zeta(2k) are transcendental (actually of the form a rational number times a power of pi). However, Euler couldn't figure out how to compute the zeta(2k+1). We still do not know how to do it, and few things are known about these numbers. That's why Apéry's Constant is named after him: Roger Apéry proved zeta(3) was irrational in 1978. The Wallis product, 27, gives an expression of pi as a product of rational numbers. It can be found using Wallis Integrals and some induction - something a first-year math student can understand. Brun's constant, 29, is named after Viggo Brun for a reason. The sum of the reciprocals of prime numbers is infinite, which means there is "at least a few" prime numbers. Viggo Brun developed a method of proof that enabled him to show that the sum of the reciprocals of twin primes is finite, which means that there are "not many" twin primes and is a significant result in number theory. That's why the constant is named after him, but the video doesn't tell you that. Also, Legendre's constant, 20, is an example of how "some constant" turned out to be 1. The theorem that gives this result is known as the prime number theorem and is the first major result in understanding the distribution of prime numbers. The Copeland-Erdos constant, 41, is interesting because Erdos and Copeland proved it contains all possible finite strings of digits (and does so in a "uniformly distributed" way, it is called a normal number), much like the Champernowne constant, except it is not obvious that concatenating all prime numbers does that. I hope I have convinced you that constants are not random numbers mathematicians make up to get their name on something.
Pure math does not need to be useful. It's math for the sake of math. Like it or not, that's how math has evolved since ancient Greece; then, occasionally, some other people realise that some of these concepts are actually useful, and something great is made. For example, the Internet technology you are using is all based on calculus, a field which was basically created by mathematicians and physicists in the 17th century for the sake of, well, math and physics, without looking for applications.
I love how my secondary favourite number is a constant, too. It is 72. And I sometimes change my first favourite number but the second one is 72 point 0000.... and its decimals go on forever.
11:31 That’s a really long equation. I have an equation that’s structured from highest degree to lowest degree and is a polynomial equation and the powers descends lower and eventually approaches to the power of 0 but technically 1 as my equation has “to the power of 0” to be inferred.
Laplace limit has nothing to do Kepler's law. It is the limit of one method of approximating a solution to the equation you showed. Exact solutions can be found numerically by other methods.
Ah the π Pi can accompany side by side the X as long as its diagonal and start at 5, because the Pi and the X or matter of matrix are both continuous numericals, one for continuous number and one for continuous calculation of the Prime counting function and both can settle together for a while at the Legendre's constant of B=1. Something, like Lennon Legend and Yoko one. You gave me an idea Sham Lahm more than you can imagine. Thanks. That pauses my comments.
Until now, i still wonder why is the Super Golden Ratio and the Reciprocal Fibonacci Constant has the same lowercase letter of Psi but yet has different values. Same for constants that uses lowercase Tau, and lowercase Rho
Nah those mathematicians are just juggling up numbers randomly to see what happens. It's like "Oh look, a 1! Let's hang it on a tree and see what happens"
Introducing "t" ; Tribonacci Ratio ; The "Real & Positive" solution/answer to equation: t^3= (t^2+t+1) is t={1+(19-3√33)^(1/3)+(19+3√33)^(1/3)}/3 = 1.8392867552...or t^3 ={1/(2-t)} = 6.2222625226.. Then : { π / e }^3 = t •( t -1) = ( t +1)/t ; with tolerance of less than 5 ppm. (1/204,876)
That's the Greek letter ψ (psi). Mathematicians like using letters from the Latin and Greek alphabets to name stuff. There are only finitely many letters to go around, though, so some things get the same name. We usually try to avoid giving two things the same name if it would cause confusion, like if we'd want to use both of them in the same equation.
3:42 : to refind the sum from the arith mean we do 3*5 = 15 , but to refind the sum from the geo mean, how we do ? 2.605^5 = 120 :/ (btw what is so the means we need to use for mean^number_of_elements = the sum ? )
So the Golden Ratio is like Superman and the Supergolden Ratio, Golden Angle, Magic Angle, Silver Ratio, Plastic Ratio, Tribonacci Constant and Viswanath's Constant are like the rest of the Justice League trying to make themselves look useful.
I have an original equation that’s structured “like” the conway’s constant except for it being used for something else but hey, maybe it’s useful or not. It’s from highest degree to lowest degree and is a polynomial but the length of the equation is determined by the range and values of x and y. The exponents are condescending order, and eventually approach to the power of 0 or 1 as the power of 0 in my equation can be inferred as anything to the power of 0 = 1.
even I, as a person who barely speaks English, understand every explanation and the essence of these constants this is the beauty of mathematics, it will be understood by two completely different people or maybe two completely different creatures maybe mathematics will become a way to communicate with aliens
btw guys did you already know the alt formula to generate Fibonacci numbers? if you didn't, well I've seen the formula in an old encyclopedia my mom had.
In your golden angle equation, alpha and beta should be swapped. Thank you for the excellent video!
The ratio between a League of Legends player’s ego to their elo is called the “Feeder’s Constant” and is approximated to infinity. It is represented by this equation and symbol: Ego/Elo = ∞. Curiously, the difference between both variables Ego and Elo, commonly referred to as the “Inter’s Gap” is also equal to infinity: Ego - Elo = ∞. This paradoxically converging phenomenon is known as the “Bronze-Iron Effect”.
Wtf bro 😂😂😂
Theorem: Let G=(X,Y) be an ranked game, where X (also knows as allied team) and Y (also knows as enemy team) are sets with cardinality 5.
(i) If X contains a Yasuo player then its death count sequence approachs to Infinity.
(ii) If Y contains a Yasuo player then its kill count sequence approachs to infinity.
Proof: We will prove only (i), (ii) is left as an exercise.
We know that G is a ranked game and X contains a Yasuo main so by Incarryable theorem (Leonard Faker, 1953) we have that the kill count sequence follows the formula K = 2^t, its trivial proof that diverges to Infinity.
Q.E.D
@@joaquingrazi2267 unironically just apply Game Theory to League of Legends vro
You can also get the value this way :
If their IQ is nearing 0 then their ego is usually represented as such :
Ego = Limit(x=> 0+) 1/x ~ infinity
0+ being any value that approach 0 from right side
Inf/0
Mathematicians really just be f*ckin with numbers to see what happens lol
In effect, yes. The magic is the applications that can arise. The amount of applications euler's number opened up were amazing, especially due to it being originally studied as an oddity in old Logarithm tables.
Yes, that's pretty much what (pure) math is.
mess around and find out
@mr.duckie._. "the difference between science and messing around is writing it down"
the cool thing about math is that you (usually) dont need super expensive shit to mess around
well stop cussing
Mathematics is a hobby. I believe much of these constants emerged because mathematicians experimented with numbers to see what kind of equations they are going to get
2 things from me to you:
Correct! And this is called: “Number theory” which explores the property of numbers, variables, constants, and irrational numbers that have unique properties.
Another thing is that most of these are from either accidents or coincidence and then eventually their work gets recognized and published to the public + recognition.
Yep! All good science and math is a hobby. Google Feynman.
@@stevejohn7459🤓
There are constants literally named after materials followed by 'ratio'. They're literally obviously Messing around and finding out
Lets create the wooden ratio
Everyone with graphical calculator has just made up random functions to see what they draw
These numbers really look like "f**k around and find out" perfect examples.
these mathematicians are really desperate to get numbers named after them
Not too late to get CrownVirtual's constant!
@@SuryaBudimansyah im working on it give me a second
I don't think so. I think it is the beauty of what they seek. Most fame comes posthumously anyway.
Most of the time scientists and mathematicians don't name their discovery after their name
It's because Euler and Gauss called dibs on all the good constants. 😂
What I've learned is when you want to give your name to something, you can by doing random shit
Nah, usually people do at least something to get their name on a constant, for instance Brun's constant (7:32) is named after Viggo Brun because he invented a new proof method to prove it is finite
most of these constants have mathematical usefulness in one proof or the other and were not made up for sheer fun even if it appears that way in this video
It's only random to you because you're shit at math
I'll start calling that the "Yorl Law"
1:51: The Magic Angle is exactly half the tetrahedron angle of 109,47°, which is arccos(-1/3) or 2 arctan(√2). Which means that the Magic Angle is exactly arctan(√2).
What is allways amazing to me, is how many of those seemingly random "useless" constants can be found in natural sciences (next to the natural constants), makeing their discovery and exploration of their behaviour exceedingly relevant.
1:31 I was prepared for it to be the bronze ratio
Same
Fr bro tf is a plastic ratio 😭😭 we got global warming ratio 😭🙏🙏
These constants are truly remarkable. And beautiful. And you introduced them so well. I played this video several times to savor the math. Thanks!
Yes, many have a possible use, but some are so artificial that they're just farcical.
3:03 imagine dying to a crazy dude for suggesting a mathematical idea, only for the suggestion to later have HIS name
One of the constants that I really like and I think you missed is, historically, a number that is described quite a bit after pi is described
The humanity's first attempt to extend their number system
It's the constant zero!
//
Also regarding Dottie's number, it is probably also one of the constant that us nerd's accidentally stumble on while we were a child: noticing that pressing cos repeatedly on a calculator makes the number converge.
Dottie's number is the solution of cos x=x in radians.
15:52 looks like logarithmic growth
Or harmonic numbers
5:12 So I guess the term "Legendre's constant" is just an overly complicated way to say "1"?
Edit: Thanks for Legendre's constant like!
some of these look like mathematicians making constants for the sake of making them which is something i would love to do
mathematicians just be inventing new shit
Yes
Agree 🫡
Love the video, great animations. But I have a question.... Is anything past like 22 actually useful in maths? Sounds like I could come up with a random sequence, then calculate a constant.. now it's useless...
I have quite some research ahead of me.
This question actually deserves a thoughtful reply.
This sentiment is something that students who are farther along in their studies, specifically in pure math, need to make peace with as it's not a given what 'useful' math is.
In short, these feel like a vague jumble of facts, especially when presented in this rapid fire format - it's hard to see the beautiful applications of them, sort of like reading the dictionary, you don't get all the beautiful synthesis of language from that!
It depends on what you mean by "useful", but some of these are meaningful.
Apéry's Constant, 26, is zeta(3). The zeta function is a very famous function used in number theory, and studying it helps us understand the distribution of prime numbers. Historically, a problem known as the Basel problem was basically "compute zeta(2)". Euler solved it, and even computed zeta(2k) for any positive integer k. It turns out all zeta(2k) are transcendental (actually of the form a rational number times a power of pi). However, Euler couldn't figure out how to compute the zeta(2k+1). We still do not know how to do it, and few things are known about these numbers. That's why Apéry's Constant is named after him: Roger Apéry proved zeta(3) was irrational in 1978.
The Wallis product, 27, gives an expression of pi as a product of rational numbers. It can be found using Wallis Integrals and some induction - something a first-year math student can understand.
Brun's constant, 29, is named after Viggo Brun for a reason. The sum of the reciprocals of prime numbers is infinite, which means there is "at least a few" prime numbers. Viggo Brun developed a method of proof that enabled him to show that the sum of the reciprocals of twin primes is finite, which means that there are "not many" twin primes and is a significant result in number theory. That's why the constant is named after him, but the video doesn't tell you that.
Also, Legendre's constant, 20, is an example of how "some constant" turned out to be 1. The theorem that gives this result is known as the prime number theorem and is the first major result in understanding the distribution of prime numbers.
The Copeland-Erdos constant, 41, is interesting because Erdos and Copeland proved it contains all possible finite strings of digits (and does so in a "uniformly distributed" way, it is called a normal number), much like the Champernowne constant, except it is not obvious that concatenating all prime numbers does that.
I hope I have convinced you that constants are not random numbers mathematicians make up to get their name on something.
@@hadrienlondon4990All you convinced me of is that all the other ones were just made up for no reason
@@jzmc7562 me not providing a reason for a constant existing in one comment =/= no reason exists
Pure math does not need to be useful. It's math for the sake of math. Like it or not, that's how math has evolved since ancient Greece; then, occasionally, some other people realise that some of these concepts are actually useful, and something great is made. For example, the Internet technology you are using is all based on calculus, a field which was basically created by mathematicians and physicists in the 17th century for the sake of, well, math and physics, without looking for applications.
This video is incredibly well-researched. Amazing job
math is the only reason i haven't become mentally unstable :]
Huge disappointment for omitting the Feigenbaum constant.
Even feigenbaum's alpha constant is missed. The tetranacci, pentanacci, hexanacci and heptanacci constants too.
He alsobmissed my favorite constants 41,83, 73 and 1007
I got the power 19-20
tetranacci was there
Mathematicians are just like: If a number doesn't exist lets create it for some reason
Bro why is this channel SO UNDERRATED?!?!!
IDK bro
IDK~
DO MORE PARTICULAR LIFE WOTH CIRCLES MORE
Look-and-say series looks gibberish yet its usage is remarkable.
seeing the golden ratio become the sliver ratio into the plastic ratio was so funny idk why 😂
What about the bronze ratio?
Great video! Someome know how does he creates the animations of the video? Seems incredible.
I would've gone absolutely bonkers for this video when I was 12
5:07 He missed his chance to call it “The Legendary Constant”
Your videos are so valuable. Really outstanding. Thanks.
Kinda ironic how Pythagoras, who denied the existence of irrational numbers, has an irrational constant named after him
These are beautifully created. What software do you use? It’s so good.
The look-and-say sequence is really trippy.
More videos like this please it’s really satisfying
Thank you, my maths teacher never stood a chance
This video helped me understand most of the constants
good work ! crystal clear illustration !
"I think my brain just committed suicide"
I love how my secondary favourite number is a constant, too. It is 72. And I sometimes change my first favourite number but the second one is 72 point 0000.... and its decimals go on forever.
every whole number is a constant
He’s back!
Mathematicians: Nah ,we're tired of numbers and symbols. LETS USE LETTERES IN ITALICS
Eggman: Who took my Chaos Emeralds?
The Super Golden Ratio:
Heard of a fair few. Only used a handful ever. Most are wild as hell to me.
4:15 No, the Euler-Mascheroni constant is what that distance approaches as you go further and further to the right.
Wow 😮😮 literally very interesting bro
That phytagorean sequence, was that a letters like the starwars introduction movie essay while theres numbering below of railroad couriering in space.
Thank you for this wonderful presentation.
as someone who knows a lot of tricks from math competitions, holy crap the universe has a lot of tricks.
El video: Habla de cosas muy, pero muy interesantes
La descripción: Números que son especiales
i don't know why i like watching these videos
Your videos are great.
A good way to pick passwords is to use a random offset and lenght in a random irrational math constant.
amazing video
this is complicated... but still better than revising for my math exam :)
This is a guide. Each constant is literally a complete course
The series consisting of the reciprocals of exponents of mersenne primes converges to around 1.4482
11:31 That’s a really long equation. I have an equation that’s structured from highest degree to lowest degree and is a polynomial equation and the powers descends lower and eventually approaches to the power of 0 but technically 1 as my equation has “to the power of 0” to be inferred.
Thanks now I can understand esoteric writing of math.
Thank you so much for making this video, I can learn more constant :D
Laplace limit has nothing to do Kepler's law. It is the limit of one method of approximating a solution to the equation you showed. Exact solutions can be found numerically by other methods.
2:32 my mind is about to explode any minute now
Great one 👌 👍 👏 😂😂😂😂😂
You know how to use manim in the correct way👌
Ah the π Pi can accompany side by side the X as long as its diagonal and start at 5, because the Pi and the X or matter of matrix are both continuous numericals, one for continuous number and one for continuous calculation of the Prime counting function and both can settle together for a while at the Legendre's constant of B=1. Something, like Lennon Legend and Yoko one. You gave me an idea Sham Lahm more than you can imagine. Thanks. That pauses my comments.
Hopefully you didn't abandon your channel and are just doing something more important rn lol, anyways great content which has so far come out
Until now, i still wonder why is the Super Golden Ratio and the Reciprocal Fibonacci Constant has the same lowercase letter of Psi but yet has different values. Same for constants that uses lowercase Tau, and lowercase Rho
No bullshit
Straight math constants
Subscribed
Makes me wonder how many of these were actually made for solving problems and how many just came from mathematicians having a little fun
it's interesting that all these constants are derived from the 4 basic forces of nature.
Nah those mathematicians are just juggling up numbers randomly to see what happens. It's like "Oh look, a 1! Let's hang it on a tree and see what happens"
Sir, now I know what these are. But I don't even know what are these used for.
Trying too digest all of this information tells me i have had a learning disability all of my life.
7:25 what does the bottom converge to? and what happens if it’s done other way around, like 1 - square root 2 + cube root 3 etc
i remember the look and see sequence from a logic riddle... i figured it out
Bro you forgot 2
pi,tau and then e
tau is the 2nd one
@@user_cy1ernah, the constant 2
2 is a constant technically
@@masonboone4307 lol
Not only 2, he forgot 37, 61 and my beloved 83!!!
That Tribonacci sequence binary zero double and binary 1 double and alternate of even and odd, when will the queen be seen if alternate?
Amazing video!
Niven's constant seems fascinating
why is the constant the thirteenth root of 253440? (4:03)
Introducing "t" ; Tribonacci Ratio ;
The "Real & Positive" solution/answer to equation: t^3= (t^2+t+1) is t={1+(19-3√33)^(1/3)+(19+3√33)^(1/3)}/3
= 1.8392867552...or
t^3 ={1/(2-t)} = 6.2222625226..
Then : { π / e }^3 = t •( t -1) = ( t +1)/t ;
with tolerance of less than 5 ppm. (1/204,876)
Golden ratio + L
You L+Problem+Issue+Skill Issue+Cannot pay taxes+bill not payed+bad+mean+lol @aaron_1112
Why is super golden ratio symbol the same as reciprocal Fibonacci constant
That's the Greek letter ψ (psi). Mathematicians like using letters from the Latin and Greek alphabets to name stuff. There are only finitely many letters to go around, though, so some things get the same name. We usually try to avoid giving two things the same name if it would cause confusion, like if we'd want to use both of them in the same equation.
3:42 : to refind the sum from the arith mean we do 3*5 = 15 , but to refind the sum from the geo mean, how we do ? 2.605^5 = 120 :/ (btw what is so the means we need to use for mean^number_of_elements = the sum ? )
10:18 : and how from the agm we get the sum ?
So so useful
0:57 I found this out in my school as a little drawing on the paper
Great video as always
So the Golden Ratio is like Superman and the Supergolden Ratio, Golden Angle, Magic Angle, Silver Ratio, Plastic Ratio, Tribonacci Constant and Viswanath's Constant are like the rest of the Justice League trying to make themselves look useful.
Which software do you use for making video please?? Maybe I want to make video in my language please
www.manim.community/
Hello, I am a math teacher and I wouldlike to be able to create such animations for my students. How can I do ? What software(s) should I use ?
Really useful thanks
shoutout to erdos showing up in half these constant names
Wao! This is amazing!
Is the sqrt(3) there? It’s the height and area of an equilateral triangle with side lengths 2
And is also the long diagonal of a unit cube
11:31 who found that polynomial in the first place???
Tribonacci sequence? What about the tetrabonacci, pentabonacci, hexabonacci and so on?
11:28 conway’s constant
I have an original equation that’s structured “like” the conway’s constant except for it being used for something else but hey, maybe it’s useful or not. It’s from highest degree to lowest degree and is a polynomial but the length of the equation is determined by the range and values of x and y. The exponents are condescending order, and eventually approach to the power of 0 or 1 as the power of 0 in my equation can be inferred as anything to the power of 0 = 1.
that's your fave? smh
I never knew what is meant by pi.
Thanks
even I, as a person who barely speaks English, understand every explanation and the essence of these constants
this is the beauty of mathematics, it will be understood by two completely different people or maybe two completely different creatures
maybe mathematics will become a way to communicate with aliens
I hope not
btw guys did you already know the alt formula to generate Fibonacci numbers? if you didn't, well I've seen the formula in an old encyclopedia my mom had.
Amazing video! no fine-structure constant though :(
@@ImperialFold Probably because it's only a list of mathematical constants, not physical constants.
1:41 if a≈137.5⁰,
then a180⁰
and then 360⁰/a>1 and a/b
3:56 shouldn't it be aproximately 2.7 since its 268545...