Every Important Math Constant Explained
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Timestamps
0:00 π (pi)
0:37 e
1:09 i = √(-1)
1:46 √2
2:27 √3
3:03 φ (phi)
3:50 Sponsor Break
4:18 γ (gamma)
4:44 First Feigenbaum constant
5:27 Second Feigenbaum constant
6:09 ζ(3) (Apéry's constant)
6:58 λ (Conway's constant)
7:49 K (Khinchin's constant)
8:41 A (Glaisher-Kinkelin constant)
9:21 Zero
10:16 Aleph Null (ℵ₀)
11:08 G (Catalan's constant)
Thanks for watching.
- Sources -
en.wikipedia.org/wiki/E_(math...)
en.wikipedia.org/wiki/Catalan...
en.wikipedia.org/wiki/Imagina...
en.wikipedia.org/wiki/Golden_...
en.wikipedia.org/wiki/Euler%2...
en.wikipedia.org/wiki/Feigenb...
en.wikipedia.org/wiki/Khinchi...
- DISCLAIMER -
This video is intended for entertainment and educational purposes only. It should not be your sole source of information. Some details may be oversimplified or inaccurate. My goal is to spark your curiosity and encourage you to conduct your own research on these topics.
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Just a quick error on your side regarding “e” : the number wasn’t actually named after Euler, it just so happened that he was working on several different numbers at that time and named them “a”, “b”, and so on. The fact that the only number that ended up mattering was named “e” is purely coincidental.
That's actually really cool
I heard he was only using vowels, and he used a already
While the name "e" did not come from Euler's name, the name "Euler's number" certainly did.
🤓🤓🤓🤓
bro said Rayman instead of Riemann
not a big deal dude 🙃🙃
AI is not good at proper nouns. Also note the weird way is says "Pythagoras."
That's cause everyone loves Rayman
also Fibonaki? 😂
AI is reading it..
My favourite constant is 1
Fr?😅
@@Weskool1 It's a very special number and pops up everywhere in math, has a lot of interesting properties too
Ok but
π=3
e=3
π=e
e=2
2=√2
√2=1
sin(x)=x
cos(x)=1
∫f(x)dx=c
i≈1
nah bro 0 clears
What a chad.
The fact he pronounces Pythagoras in multiple ways and doesn't get it right in any way is humorous
Aleph null ^ Aleph null is not equal to Aleph null. Aleph null ^ n = Aleph null where n is finite, but putting Aleph null as an exponent results in a larger infinity. Even 2 ^ Aleph null > Aleph null.
Not quite. We *think* that this is true, but we don’t know, we can’t prove it.
Yeah I was thinking the same thing.
a^x is O(x^∞). Or, more precisely, lim h→0 (1+hx)^(1/h), making it O(x^(1/h)) in the limiting case as h→0, or O(x^w) in the limiting case as w→∞.
If it was closed under even the most rapidly increasing elementary functions, there'd be no practical way to generate aleph 1.
@@Pro100kvOdratui you can quite easily prove that 2 ^ Aleph null > Aleph null, since you can find a bijection between a set of size 2 ^ Aleph null and a set of the cardinality of the real numbers
@@Pro100kvOdratuiNo, it is definitely known that 2^Aleph0 > Aleph0 (by Cantor's theorem). What we do not know (and in a certain sense cannot know) is whether 2^Aleph0 = Aleph1 (continuum hypothesis).
there is too many Alehp Nulls to understand this
Aleph null to the power of aleph null is continuum. (10:43)
If you're looking for a change of pace , how about every medical/surgical specialty explained
White theme: can't watch at night
Dark theme: can watch anytime
6:50 “The exact value of three is not known”
jokes on you, it’s 3
11:27 i see france
Every physics constant? Or would that take too long
This video was actually cool, I learnt a lot, you’re videos in general are interesting
Please never pronounce Pythagoras that way again
Agreed
Nice video as always 😏 Maybe can you make film about types of numbers like natural, surreal, p-adic? 😎
Thanks for the idea!
4:56 change your smoke detector bro
it sounds too stretched out to be a smoke detector
i want to but its hard to reach and im kinda lazy 🦥 😂
LOL i didn’t notice that
It feels like 0 is placed strangely late into the video. I'd have thought it'd be one of the first constants you mentioned. Also, I can't believe the number 1 didn't get a section.
By the way, I wish you'd have given τ (tau) a mention. I mean, Tau Day was only a few days ago, after all. (For those of you who don't know, the number τ is defined as the ratio of a circle's circumference to its radius, equal to 2π and approximately 6.28. The use of τ clarifies radian angle measurements; for example, 1/4 turn = τ/4 rad, 1/6 turn = τ/6 rad, and so on.)
Can you collaborate with me to make videos better? If interested, send me an email 📨
@@ThoughtThrill365 Is there money involved?
yes, pls send me an email, we will discuss.
@@ThoughtThrill365 What's your email address?
@@ThoughtThrill365Okay, what's your "mailbox", if you know what I'm saying?
(CZcams is being ridiculous right now.)
It’s like this guy actively tried to mispronounce as many names as possible.
it's the opposite, i actively tried to correctly pronounce.
I didn't know that the square root of every non perfect square is irrational. That's absolutely wild.
Yup! It's because every non-integer rational is also not an integer when squared.
This is because when a rational is not an integer, that means the denominator has something in its prime factorization that the numerator doesn't, and this doesn't change when squaring, as squaring just adds another copy to the prime factorization of both the numerator and denominator
💀
Same
@@andrewsauer2729Wow that’s actually really cool! How have I never heard of this
@andrewsaur2729
Thanks for that really clean explanation. I had a little bit of an intuition for that fact that squaring decimal numbers doesn't create integers yesterday. But I'm still astounded by that fact.
It seems like something that should have come up in a math class at some point. Like I always thought it was crazy that the square root of two is irrational and right under my nose are all these other irrational square roots.
aleph_0^aleph_0 is not aleph_0. It's the same as 2^aleph_0, in particular uncountable.
I Love all the constants
in Math because i am an Theoretical
MATHEMATICIAN. But my most favorite or i could say the most DANGEROUS ones are
0 (Holy) and the ALEHP NULL (sorry hell) !!!!!!
Because I am the type of Expert MATHEMATICAIN who don’t really understand
MATH and the
REALITY (or PHYSICS)
R u there with me???
did you drank cocaine?
My favourite is e and the chaos numbers. Although it’s said to see no talk on the monster number from group thoery
My favorite branch of Mathematics is abstract Algebra and my favorite constants are both e and pi because they share something mysterious which we don't really understand yet. I mean Eulers Identity is not a coincidence.
Pi wasn't "discovered" by one guy, Archimedes calculated its value to an impressive degree but that just represents one in a series of refinements on the known value. It was known for centuries before Archimedes by various civilizations that pi is a bit more than 3, since that isn't hard to deduce. It's harder to deduce more precise values, but I wouldn't call that "discovering pi".
"adolf kinkelin"
theres 2 things that could go horribly wrong
1:23 Show me an example of a real number that is neither rational nor irrational!
1:50 Most insane pronunciation of Pythagoras I've ever heard.
Don’t forget he said “pie-the-gore-ass” 💀
why are universal constants so small?
There is only one kind of math. Drugonometry.
Which text to speech AI do you use? It's pretty good apart from minor pronunciation errors.
bro, it's not ai voice.
@@ThoughtThrill365lol
@@ThoughtThrill365 I mean ig you can take it as a comp or a joke over some names you said being pronounced pretty uh let's just say............little uh bad.
@funwithtommyandmore i agree with you xD
@@ThoughtThrill365 :)
Weird to call it Pythagoras’ number when he was the one claiming it wasn’t irrational 😭😭😭😭
Where is Euler's number e?
My favorite branch of mathematics is probably complex analysis or fractional calculus. :3
But I don't know how much I know about them, I just like them.
e isn't named by euler
True :3
It isn't named BY Euler? No, he certainly did name the number "e".
If you mean it isn't named AFTER Euler, that's also wrong, since we commonly call it "Euler's number".
8:10 why did you draw the 1
Do you do physics too?
Yes sir
√2 is also algebraic which is nice. π for example isn't
Trigonometry is my jam
Can an irrational number be expressed as a ratio of two integers?
No, the definition of irrational numbers is the exact opposite of that.
Is “i” actually a constant? I always viewed it as an imaginary variable. I very well could be wrong though.
Everywhere I look I see Dan ~ Reform ~ .
isn't aleph null ^ aleph null = aleph one?
We don't know, maybe.
n^aleph 0 ≥ aleph 1
@@trifonmag4205 technically, we cannot say whether 2^aleph zero = aleph zero, because that is the continuum hypothesis which is undecidable (neither true nor false) in ZFC
That is what I remember. I believe the book was Asimov on Numbers from a long time ago. But maybe we learned more in the last 40+ years!
I love probabilities
i like your videos the pronunciation is funny though
11:00 No, it proves that the size of rational numbers is the same as the natural numbers.
What about-1/12?
It's a number, for sure.
what about the gravitational or Coulombs constant
I think this video is about numbers, not physical constants.
i is not *the* square root of -1. It is *a* number that satisfies i^2 = -1. Technically, i can't be distinguished from -i.
π = C/d
8:51💀
Quantem
the question that bothers me is why is pi an irrational number if it is defined as a ratio. Rational numbers are can be defined as ratios.
It is a ratio of two quantities, but one of those quantities is not an integer. To be rational it would need to be a ratio of two integers
If 0 = 0 + 0i then 0D = 0D + 0Di.
I like algebra
perimetros means perimeter, not circunference
The perimeter of a circle is its circumference.
These are exactly the same
11:51 Don't you mispronounce Ramanujan's name! I admire that mathematician!
Electrical engineers do *not* use i! (We call it j, because i is already used for electrical current.)
i factorial?!?
That means you use the number i, and you use the symbol i; you just don't use the latter for the former.
Aleph NO?
Or is that Aleph-zero or Aleph-nought?
“Aleph Null”
you forgot 4
algebra
π
Bro said fee for phi
ｈｅ ｄｉｄ ｎｏｔ．
You forgot tau.
Yes but it's just simply pi squared nothing really special
@@funwithtommyandmore pi squared? i think you mean 2pi
@@funwithtommyandmoreYou mean 2π.
Also, τ is defined as the ratio of a circle's circumference to its radius, which is a definition completely independent of π. You can't discount τ just because it's a nice multiple of a constant we'd already defined.
Bruh
AI voice or dyslexia?
fucking rayman bruh
Yeah pronunciation is not…. His strong suit….
Is it just me or did bro sometimes change his pronunciations? Bifurcation is an example…
At 11:05 you have showed the proof that the set Q of rational numbers has the same cardinality as the set N of natural numbers, and you haven't showed the diagonal method proof for the set R of real numbers.
I was the first person here but eh
Please change the batteries on your fire alarm
While geometry and calculus are closely related, interestingly, chaos theory is not as far as we know. In this respect chaos theory resembles gravity in unified field theory in physics.
Sorry to be that guy, but you forgot a few...
Every other metallic ratio
The supergolden ratio
The plastic ratio
Liouville numbers
Transfinite numbers
Chaitin's constants
Prime constant
Omega constant
Cahen's constant
Erdős-Borwein constant
The lemniscate constant
The 12th root of 2
ln(2)
And quite a few others
Yes, I suppose the video is poorly titled.
The constant mispronunciations are distracting.
Are you trying to mispronounce every word? lmao
no real person narrating = no subscription.
If it's not real person then who is it? It's a human voice. Nowadays, everyone is accusing everyone about their voice.