I've seen Euler's Identity written as e^iπ + 1 = 0, which I think is the most beautiful version of them all, because it uses the fifth most important number in mathematics, 0.
Euler's identity is derived from Euler's formula, which is as follows: e^(iθ) = cos θ + i sin θ. Evaluating at θ = τ, we get e^(iτ) = cos τ + i sin τ, which reduces to e^(iτ) = 1 + 0i. There you go. 0.
I saw a cool problem you could cover. If a fly is inside of a train and both are going north is the fly flying faster than the train. I’ve talked about this problem with my family and we couldn’t come up with an answer. Hope you like the question.
In order to answer this, we must specifically define what it means to be going "faster" than something else. The entire answer hinges on the choice of definition. The key detail here is that motion must be defined with respect to a fixed reference point. In everyday usage, this reference point is usually Earth. So, if the train is moving at some positive speed A with respect to Earth, and the fly is moving at some positive speed B with respect to the train (which I assume is implied to be less than A), then the fly is moving at some positive speed A + B with respect to Earth, and A + B must be greater than A. So if you use Earth as your reference point for everything, the fly is moving faster than the train. Ultimately, this question boils down to: do you want to use B as the fly's speed, or do you want to use A + B? It's just an annoying semantics riddle.
There probably proof of tau but history wise there was debate whether we should you use circumference/diameter or circumference/radius hence we end up getting pi = circumference/diameter and tau = circumference/radius. They basically just exist cause mathematicians couldn’t agree
@@roma540The measurement system? I don't know why you singled out that particular system, considering that no popular measurement system at all directly acknowledges the existence of τ.
is there any other perfect number that can also multiply all the factors together to reach the same number? 6 = 1x2x3, 6 = 1+2+3... 6 is more perfect than other perfect numbers (this is a hill i will die on)
if you include 1 you must include 6 or 28 otherwise you are rigging the rules to make perfection. And, of course if you do include them, it doesn't work. So not exactly a brilliant phenomenon, is it?
Firstly, perfect numbers hardly have anything to do with the concept of perfection. Mathematicians like co-opting existing words to name mathematical concepts, and this is a case where the choice of word doesn't carry much of a deeper meaning. Also, why do you prefer your definition anyway? Perfection is not a well-defined mathematical concept. But if you really believe in your definition, I guess I'll list all the numbers it captures: 1 And there we go. A positive integer that is the sum of all of its divisors except 1 and itself is not known; if any exist, they must be very large. So our current list is empty, which doesn't capture the imagination very much either. Also, "rigging the rules"? What form of fraudulent conduction is occurring here, exactly? A core part of math is inventing new rules and seeing where they take you; what business of yours is it to tell other people what rules they can or cannot invent? But if you must play it your way, fine. "A perfect number is a positive integer equal to half of the sum of ALL of its divisors." Amazing.
Tau exciting!
Was just thinking this!
This would have been the best!!! Next year!
Tau looks important. I would put a box around it.
😅 how exciting
@@mzoxololinda8408 And 69 likes right now, so nobody touch that button anymore!
Today's my birthday! Glad I'm discovering this interesting math fact!!
We share a birthday 😮
Three birthdays?
oh nice, the same here
Same here!
Same here!
Wooo Tau Day!! Although in Asia it’s 6/29 now
In russia too
@@darm3k technically Russia is mostly part Asia
@@thatonedynamitecuber wtg? Did you just assume his continent? Nah that's crazy.
@@egaLwie. I know most Russians live in the Europe part, but I’m not assuming he’s european or Asian.
And in Oceania
Edit: but written as 29/06
People that are already in June 29 be like
I've seen Euler's Identity written as e^iπ + 1 = 0, which I think is the most beautiful version of them all, because it uses the fifth most important number in mathematics, 0.
Euler's identity is derived from Euler's formula, which is as follows:
e^(iθ) = cos θ + i sin θ.
Evaluating at θ = τ, we get
e^(iτ) = cos τ + i sin τ,
which reduces to
e^(iτ) = 1 + 0i.
There you go. 0.
Que MARAVILHA!. Thanks for sharing.
It's the 29th here today but the 28th is a genuine holiday in New Zealand so I'll bookmark it for next year.
I saw a cool problem you could cover. If a fly is inside of a train and both are going north is the fly flying faster than the train.
I’ve talked about this problem with my family and we couldn’t come up with an answer. Hope you like the question.
In order to answer this, we must specifically define what it means to be going "faster" than something else. The entire answer hinges on the choice of definition.
The key detail here is that motion must be defined with respect to a fixed reference point. In everyday usage, this reference point is usually Earth. So, if the train is moving at some positive speed A with respect to Earth, and the fly is moving at some positive speed B with respect to the train (which I assume is implied to be less than A), then the fly is moving at some positive speed A + B with respect to Earth, and A + B must be greater than A. So if you use Earth as your reference point for everything, the fly is moving faster than the train.
Ultimately, this question boils down to: do you want to use B as the fly's speed, or do you want to use A + B? It's just an annoying semantics riddle.
so is there some sort of proof for tau? or is just a different pi that is multiplied by 2?
There probably proof of tau but history wise there was debate whether we should you use circumference/diameter or circumference/radius hence we end up getting pi = circumference/diameter and tau = circumference/radius. They basically just exist cause mathematicians couldn’t agree
It's defined as the ratio of a circle's circumference to its radius.
I didn’t have a pi, so I ate double ice-cream today and it was perfect.
You didn't talk about how it's my birthday, but I'll let it slide ;p
Why am I watching this video now? My 28th birthday was on June 28th 😂
Wouldn't 12/12 also be a perfect number day?
Also 12/06 and 06/12
Indeed, how exciting
dude, learned something new today. I am very happy. Happy day!
29th of June for 5 hours now, still gonna watch this exciting video.
HAW HAW you're not in the US and the date doesn't work anyway.
14:26 still watched
that's a deep voice
i loved tau you explained this beautiful occurrence in tau universe
Me, whose birthday is this day:
🎈😢 Oh that's why everyone is celebrating
6/28 is my birthday, how exciting
Hey I don't know if you'll read this but 6/28 is my birthday too 🎉
How can you be handsome and smart at the same time 🙄
Eye roll emoji?
I thought you were gonna say it’s a double math holiday because it’s pi day x 2. 3.14 x 2 = 6.28
π & τ should change so that τ is half of pi because ττ looks like π
How do you type this tau charester? (sorry for bad english)
@@Sasha123-d1qIt's included on some keyboards. If it's not on yours, you can probably copy and paste it from the internet.
You should make more random geometry questions fully explained out like the ones you previously did
also happens to be my birthday
I love you
Happy Tau Day, for the greater good. :^)
**Angry imperial noises**
@@roma540The measurement system? I don't know why you singled out that particular system, considering that no popular measurement system at all directly acknowledges the existence of τ.
@@isavenewspapers8890 My god, that is an excellent accidental joke!
But no, original comment was making a Warhammer 40k reference, and so did I
@@roma540 Oh, I see! That's pretty epic, honestly.
You got anything for 8/29? 😇
Wow didnt know that euler identity could be modified like this!
I definetly like that version more
1 is better than -1 😅
Can't wait for alternate pi day on 22nd July for all countries but those who write the month first
Tau is much amazingness 😎
Bro forgot to call it 2π day
:|
How exciting 😳
I only just now noticed that Tau is the right-half of the pi symbol
Happy holidays!
3:02 Missed "Tau exciting" opportunity
Exactly!
Happy tau day
You only let us know when there's merely hours left to celebrate!!
Hi
So Tau is equal to your dad (tu pai)?
Well, if it is to mix with latin, then it is "two pee".
i prefer 7/27 more
I notice perfect numbers alternate ending in 6 and 8
is there any other perfect number that can also multiply all the factors together to reach the same number? 6 = 1x2x3, 6 = 1+2+3... 6 is more perfect than other perfect numbers (this is a hill i will die on)
Double Pi day
if you include 1 you must include 6 or 28 otherwise you are rigging the rules to make perfection. And, of course if you do include them, it doesn't work. So not exactly a brilliant phenomenon, is it?
you dont seem to get it
Firstly, perfect numbers hardly have anything to do with the concept of perfection. Mathematicians like co-opting existing words to name mathematical concepts, and this is a case where the choice of word doesn't carry much of a deeper meaning.
Also, why do you prefer your definition anyway? Perfection is not a well-defined mathematical concept. But if you really believe in your definition, I guess I'll list all the numbers it captures:
1
And there we go.
A positive integer that is the sum of all of its divisors except 1 and itself is not known; if any exist, they must be very large. So our current list is empty, which doesn't capture the imagination very much either.
Also, "rigging the rules"? What form of fraudulent conduction is occurring here, exactly? A core part of math is inventing new rules and seeing where they take you; what business of yours is it to tell other people what rules they can or cannot invent?
But if you must play it your way, fine.
"A perfect number is a positive integer equal to half of the sum of ALL of its divisors."
Amazing.
@@isavenewspapers8890 than you for making my point so eloquently.
😮
Tripple, in Madeira we celebrate São Pedro
Wow
Honestly, if not for the goofed up Presidential Debate between Trump and Biden, I would appreciate Tao a lot more.
I see no reason to let the presidential debate influence your judgement.
That’s my Birthday!
Tau symbolically is 1/2 Pi but its value is twice Pi.
Or maybe the legs of Pi is 'n' in '1/n'. And then, Tau is '1/1'.
Oh, I made 2 pies already. How funny.
I love u
Today is National statistics day in India, celebrated in memory of Prof. P C Mahalanobis, known as father of Indian Statistics
June 28, 2024: The best day of my life.
-4 artists release their musics
-t a u .
-perfect numbers
Perfect Number Day! 🎉
Are we going to ignore that 6 isn’t just 1+2+3, but also 1*2*3?
6 puts other perfect numbers to shame.
👇 Tau over Pi gang‼️💯💯💯
2pie day
Can't celebrate Tau Day without pie...or should I say pi.
Why not
:D
it's crazy how e^iτ=1
from now this is my favorite equation
Also 8-2=6
Tau > pi
It’s kind of weird you didn’t mention 69 after 4/20.
69 days after 4/20
Why do you say "one fourth", yet 25¢ is a quarter? I say a "quarter" of the circumference. I find this genuinely odd.
All the best.
The phrases "a fourth" and "a quarter" are both extremely common in the English language.
Not exciting
No you
ruclips.net/user/shortsNDhnfyGSZUU?si=ZpNTjRJ9waxo0dpD
How high did he actually get?