Every Important Math Constant Explained
Вставка
- Опубліковано 4 лип 2024
- Take the Quiz here: studygeniuspro.com/create-gam...
The quiz checks how much you remember from the video and if you get over 70% right you get to try cool AI features for free without registration!
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.
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..
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.
🤓🤓🤓🤓
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.
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
The fact he pronounces Pythagoras in multiple ways and doesn't get it right in any way is humorous
If you're looking for a change of pace , how about every medical/surgical specialty explained
Aleph null to the power of aleph null is continuum. (10:43)
Please never pronounce Pythagoras that way again
Agreed
Every physics constant? Or would that take too long
6:50 “The exact value of three is not known”
jokes on you, it’s 3
11:27 i see france
It’s like this guy actively tried to mispronounce as many names as possible.
it's the opposite, i actively tried to correctly pronounce.
White theme: can't watch at night
Dark theme: can watch anytime
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???
This video was actually cool, I learnt a lot, you’re videos in general are interesting
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?
(UA-cam is being ridiculous right now.)
aleph_0^aleph_0 is not aleph_0. It's the same as 2^aleph_0, in particular uncountable.
Nice video as always 😏 Maybe can you make film about types of numbers like natural, surreal, p-adic? 😎
Thanks for the idea!
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.
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
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.
isn't aleph null ^ aleph null = aleph one?
We don't know, maybe.
n^aleph 0 ≥ aleph 1
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.
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.
11:00 No, it proves that the size of rational numbers is the same as the natural numbers.
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.
√2 is also algebraic which is nice. π for example isn't
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.
why are universal constants so small?
11:51 Don't you mispronounce Ramanujan's name! I admire that mathematician!
Trigonometry is my jam
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".
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 :)
i like your videos the pronunciation is funny though
what about the gravitational or Coulombs constant
I think this video is about numbers, not physical constants.
If 0 = 0 + 0i then 0D = 0D + 0Di.
What about-1/12?
It's a number, for sure.
Can an irrational number be expressed as a ratio of two integers?
No, the definition of irrational numbers is the exact opposite of that.
I love probabilities
perimetros means perimeter, not circunference
The perimeter of a circle is its circumference.
These are exactly the same
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.
Do you do physics too?
Yes sir
Aleph NO?
Or is that Aleph-zero or Aleph-nought?
“Aleph Null”
you forgot 4
Bro said fee for phi
I like algebra
AI voice or dyslexia?
Is it just me or did bro sometimes change his pronunciations? Bifurcation is an example…
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.
fucking rayman bruh
Yeah pronunciation is not…. His strong suit….
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
Bruh
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.
Please change the batteries on your fire alarm
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.