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
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.
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.
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.
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).
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.
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
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.
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.
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)
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… how many constants are there? Named ones I mean. I’m sure there’s an infinite amount but I want to know how densely packed they are on the number line.
If you mean that the Champernowne constant's decimal representation contains the full decimal representations of all the other numbers, this is incorrect. For example, 1/3 is 0.333... . There is never a point in the Champernowne constant where it just enters an infinite string of 3's in a row without any other digits, so 0.333... is not included in the Champernowne constant.
5:06 - His name is "Adrien-Marie Legendre" (pronounced "Add-ree-on Ma-ree Luh-zhon-druh"), not "Adrian Murray Legendary" (even though he is quite a legend!)🤣
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
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"
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.
In your golden angle equation, alpha and beta should be swapped. Thank you for the excellent video!
This video helped me understand most of the constants at 12 years old. Thanks!
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.
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.
Bro why is this channel SO UNDERRATED?!?!!
IDK bro
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
These constants are truly remarkable. And beautiful. And you introduced them so well. I played this video several times to savor the math. Thanks!
These numbers really look like "f**k around and find out" perfect examples.
15:52 looks like logarithmic growth
Or harmonic numbers
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.
DO MORE PARTICULAR LIFE WOTH CIRCLES MORE
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.
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).
I would've gone absolutely bonkers for this video when I was 12
1:31 I was prepared for it to be the bronze ratio
Look-and-say series looks gibberish yet its usage is remarkable.
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!!!
math is the only reason i haven't become mentally unstable :]
Mathematicians are just like: If a number doesn't exist lets create it for some reason
Amazing video! no fine-structure constant though :(
@@abehankens7456 Probably because it's only a list of mathematical constants, not physical constants.
seeing the golden ratio become the sliver ratio into the plastic ratio was so funny idk why 😂
What about the bronze ratio?
4:15 No, the Euler-Mascheroni constant is what that distance approaches as you go further and further to the right.
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!
as someone who knows a lot of tricks from math competitions, holy crap the universe has a lot of tricks.
The look-and-say sequence is really trippy.
El video: Habla de cosas muy, pero muy interesantes
La descripción: Números que son especiales
3:03 imagine dying to a crazy dude for suggesting a mathematical idea, only for the suggestion to later have HIS name
some of these look like mathematicians making constants for the sake of making them which is something i would love to do
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.
i remember the look and see sequence from a logic riddle... i figured it out
5:00 Even Wau is included in this list!
You know how to use manim in the correct way👌
i don't know why i like watching these videos
This is a guide. Each constant is literally a complete course
A good way to pick passwords is to use a random offset and lenght in a random irrational math constant.
He’s back!
More videos like this please it’s really satisfying
2:32 my mind is about to explode any minute now
I got a bit scared cuz i did math 💀
(i got scared when aparear the video not at the symbols)
Wow 😮😮 literally very interesting bro
Mathematics is totally definitely absolutely 100% without a doubt, NOT MAGIC!!!
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 formula to generate Fibonacci numbers? if you didn't, well I've seen the formula in an old encyclopedia my mom had.
5:12 finally, we found a cooler 1.
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
9:34 My humor is so broken
I love how legendre has the number 1 named after him.
it's interesting that all these constants are derived from the 4 basic forces of nature.
Mathematician: "Hey we need a way of representing 2xπ"
Other Mathematician: "2π"
Other Other Mathematician "τ"
Everybody: "OK"
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.
Thank you for this wonderful presentation.
Finnaly
You are the first one
Thanks now I can understand esoteric writing of math.
2:10 I was so disappointed when it didn't converged to the Platinum Ratio.
What about the alpha constant? It’s approximately equal to 1/137
it's a physical constant, not a mathematical one
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.
1:53 You could've said that θ_m = arctan(√2).
1:39 angle alfa is smaller than angle beta and angle 360° is bigger than angle alfa so this doesn't make sense
You're right. Alpha and beta are swapped in the correct formula.
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
I'm just curious what led to half of those constants
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… how many constants are there? Named ones I mean. I’m sure there’s an infinite amount but I want to know how densely packed they are on the number line.
How does one even stumble on this stuff and know what it means?
Wao! This is amazing!
should've mentioned that the reciprocals of Sylvester's sequence approach 1 in summation, great video though
9:58 Infinity Symbol
11:32 💀
The constant in my purse is exactly zero (and I even do not have a girlfriend...).
Feigenbaum constants?
Very important in chaos theory
amazing video
Thank you so much for making this video, I can learn more constant :D
Hi there might be first
Also how many of.them can be calculed on desmos
Edit: I am second
Hi Digital Genius!!
At 1:40 you switched alpha and beta on the diagram. It should be the opposite .
So so useful
I think there are numbers in this video.
Great video as always
9:30 No snickering in the back of the class.
Mathematicians are so desperate to make shit up to "prove" their relevance
golden ratio remains my favorite costant
You forgot the harmonic mean, which is n / (Σ_(i=1)^n 1/xᵢ) for n values of x.
I found out about 16:00 Foias constant on my own and called it first eulerbrot constant.
i love this
if we divide overscribed by inscribed one [46, 47?] - another constant!
Still waiting for ultra super mega golden ratio
so they made us just learn all of this just because they just messed around with addition and subtraction
1:10 if a = b, this equation says 1 = 2. Am I making a mistake here?
4:04 Why aren't there plus signs between the terms?
Because the Harmonic series isn't a sum, it's a series.
@@goosemchonk A series is, by definition, an infinite sum.
@@isavenewspapers8890 nuh uh
The fact that I know 30% of them only despite being in 12th standard
So far, I know about 15-20% of them. But hey, not too far off you.
What software do you use to make these videos 😍😍
Bro next time explains every scientific constants, and clearer pls
why is the constant the thirteenth root of 253440? (4:03)
Champhernowne constant has all the other constants in it.
If you mean that the Champernowne constant's decimal representation contains the full decimal representations of all the other numbers, this is incorrect. For example, 1/3 is 0.333... . There is never a point in the Champernowne constant where it just enters an infinite string of 3's in a row without any other digits, so 0.333... is not included in the Champernowne constant.
5:06 - His name is "Adrien-Marie Legendre" (pronounced "Add-ree-on Ma-ree Luh-zhon-druh"), not "Adrian Murray Legendary" (even though he is quite a legend!)🤣
your channel banner is just √1²+0² right?
you are a genius