Transcendental Numbers - Numberphile
Numbers like e and Pi cannot be made using normal algebra.
Featuring Australia's Numeracy Ambassador, Simon Pampena.
Extra footage: • Transcendental Numbers...
More links & stuff in full description below ↓↓↓
Discussing transendental numbers, algebraic numbers, pi, e and other stuff.
Simon's website: www.numbercrunch.com.au/
Root 2: • Root 2 - Numberphile
Pi Playlist: • Pi on Numberphile
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"So it'll be 10$ sir." "You mean 10 in base 10?" -_-
every base is a base 10 :(
10 is a legit number in base 2, soo..
10 = 2 :D
"No in binary"
HAHAHA!! Genius
My favorite part of these videos is how excited each mathematician gets about their particular number. Other people feel how I feel!
Sure!
Geldarion Degana im only that happy if i see pizza
!eruS
Exactly! and their eyes shine with the light of truth.
@@maroofsultan 😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂
'7π - 22 = 0' - Simon Pampena, 2013
500 lb Pure Feminism No it equals 0.0084
Useless Tutorials t h a t i s i n d e e d t h e j o k e
Slimzie Maygen Y tho
Can you get π to 0 using the game from the video?
Rovix yeah π-π=0
Are we just gonna breeze past people dying because of the square root of 2?
pythagorean cult yo
They already did that video :P
that's kinda normal here man
too soon?
Mathias Sven a couple centuries late
You know things got serious when you're asked which base you're expressing your numbers in. :D
?
Single question mark isn't sufficient enough. Please, specify which part of the sentence you did not understand.
@@cparks1000000 10 x 10 = 100
Otakar Beinhauer it’s perfectly sufficient. I’d say he was asking what a base is, for example “what is base 10? What is a base anyways?” Trying to seem smart by not understanding something is counterproductive. Use the context clues available to you it’s not hard.
*oh I mean 10... in base pi*
I love that he said in all seriousness that if he could add to the knowledge of pi, he would die a happy man
Using a “reduce to zero game” to intuitively explain algebraic numbers is actually really smart!
IKR!
“You mean 10 in base 10?” - cheekiest comment ever made on KZhead.
That sigh at the end knowing that a good days maths has been done... :)
The sigh of QED.
"Square root of 2, you know, people died for this number" STORY TIME
The guy that discovered the square root of 2 was part of this group called the pythagoreans. They were almost religious about numbers and really really liked whole numbers like 1 and 2. Then this guy found out that the diagonal of a square with sidelength 1 was irrational and they killed him.
Capricorn it sounds funny when you listen to the story. However, just imagine getting thrown off the ship and drowning for discovering something new. That’s extremely sad.
I first watched this video when I was a freshman in High school. It blew my mind. Now I'm in Field theory almost done with undergrad and I saw the material again and I thought "That was it! That was the thing! This is what Simon was doing!" It made me very excited when I realized c:
"You cannot not like pi." Say that to ViHart.
***** Well, I guess so. Also, it was a joke.
***** Also, by that logic, 2 might as well be 1.
I'm ignoring this post. I'm not going to respond if you try to reply to me. This is just a warning, made for no one to waste time on this.
( ͡° ͜ʖ ͡° )TheNoobyGamer Um, are you talking to me? I haven't responded to you in eight months.
***** I ignored it but came back to my read notifications list since I was preparing an argument... The answer is, no. Why would I be talking to just you? I'm just telling people that contacting me now would be useless. I'm just tired of people plus one-ing my comment.
Engineers DO NOT use 22/7! I always approximate to 3.14159 if no calc. handy. EDIT: Except my mental arithmetic is awful, so really I use 3.0 and I just pretend and fiddle a bit - adding a few numbers to guess the decimal places - The bridge is still standing, but it does have a bit of a crack through the middle, and my gears are not quite round, but hey, it just makes a funny noise and fails every six months.
scrub, 3.141592 > 3.14159
elchingon12346 Do you even math, bro? The next digit after 2 is 6. Round up much?
boston922 my whole life is a lie
Though you should use 3.142 ))
(pi)^2 = g
Glad to see that Syrio Forel didn't die after all :)
ture dat :D
jajajaajajajasjajajajsasfnisujndgpijf
Season 8 he will come back
Dante C And here we are
hahahah, what do we say to deadly math problems?
When I become a teacher, I want to be a teacher like them. They are so awesome, explain everything in simple terms first, build up the concept, introduce one jargon. let that sink in, introduce another jargon and this way, they make the content much more enjoyable and engaging. Rather than jumping right into theories, playing with numbers and seeing how beautiful they can be is probably the best way to learn math. From this video, I learnt two things. 1. What is transcendental numbers 2. How to teach someone critical concept efficiently with in certain steps Thanks to everyone who were involved in the creation of this video.
I like this comment very much
@@quantumgaming9180 thank you. You'd be pleased to know that I have plans to open a youtube channel for competitive programming. I am yet a noob at this. But I could see myself doing this for a long time.
his way of teaching is unbearable. if you are to be reduced to a dummy that enjoys being told things like "1-1=0 , yey!" (for the enjoyment of his teacher) then you are beyond help!
This man is great with words. He translates sqroots to sentences and tells elaborate vibrant stories. His games transform numbers to characters. He should consider writing a book on math, or math journalism.
And also great at trying not to say physcedelic
I'm such a massive fan of how much this guy loves numbers.
It's great to see someone get so excited time and time again. You seem to love what you're doing.
11:36 If you're extra curious, the 11th root of 294,204 and the 18th root of 888,582,403 are also close approximations to pi and are in fact much closer than the cube root of 31.
Me encanta la pasión que mete este tío en sus explicaciones. Reviso estos vídeos cada año, y siempre me fascinan. Este profesor es fantástico sólo por la pasión que te transmite y con la sencillez que explica las cosas. Bravo! Saludos!!
I wish this chap had been my maths teacher! I love the way he prompts them to work it out for themselves whilst being encouraging and just...*sigh*
This is really good. It shows a piece of some more advanced math at a level where many people will be able to follow, and at the same time it touches very different branches of techniques and results in maths, all explained by a passionate and well-formulated guy. Brilliant!
"no flies on you" aweome phrase
I don't understand math much since school... But I really appreciate someone tell the concepts in such easily understandable format... Wish I had a math teacher like you
Almost 58 years old (5 days shy) and I have learned something. Thank you. I sincerely appreciate it!
There's something so charmingly intense about this man, even in the first two seconds of the video: "It's mind-blowing"
Huge fan of numberphiler and I like your style the most . Cheers mate.
9:45 "You love Pi. It comes" -Simon Pampena, 2013
Holy crap, imagine if the transcendentalist Henry David Thoreau discovered these numbers.....
***** He'd probably just dismiss it as worldly and unjust.
***** Transcendental numbers are superior to transcendentalists. Just another fact of life.
_“Counting is how we build numbers”_ _“Geometry is how we build numbers”_ _“Algebra is how we build numbers”_ and on and on again whenever new techniques are discovered
"Topology is how we build numbers" "Ramsey theory is how we build numbers" :p
Currently computing is how we build numbers
Enough of each is mutually isomorphic, so it all works out the same, essentially.
@@atimholt Eh, not quiet. Counting is algebra is combuting. Its all digital. Gemometry is fully analog, and thus can accomodate weird things that cannot be expressed as deri atives of arbitrary concretes.
@@gnochhuos645 we tell them what to do and keep having to fix their inaccuracies
If you have a function y=e^x then the value of y is always equal to the value of the slope of the tangent at that point. The best brief explanation of e ever!!
This guy's passion is contagious.
The more precise definition of transcendentals is that they are not the root of any polynomial with rational coefficients; that's why the game they demonstrate here doesn't include "multiplying it by zero" or "raising it to the zero power". The polynomials corresponding to these moves do not have unique roots. (Tell me what value of x makes the following equation true: 0*x + 0 = 0. Answer: all of them.)
Every polynomial with rational coefficients can be converted into one with integral coefficients by multiplying by a common multiple of the denominators. They will have precisely the same roots.
Even more precise definition: a complex number is transcendental if it is not the root of any _nonzero_ polynomial with rational coefficients. Of course, replacing 'rational' with 'integer' makes no difference to the definition.
@@petrospolemistis Can't tell if troll or needs to go back to school.
@@petrospolemistis Neither is 'sheep' times zero. Your statement makes absolutely no sense.
@@petrospolemistis You must be a troll, surely? You're making less sense each time. At this point you're just being silly.
Make a video on Euler's Identity!!
He was a white male, Swiss, about 5'5", which many believed to be the Zodiac killer during the 1970s.
He means e^i*pi + 1 = 0 The equation at 12:07
Ken Sarcasm?
@@mitalipandit2891 you know that is not Eulers identity its an equation that uses Eulers identity but the general form is e^ix = cos(x) + isin(x). Also if im not mistaken Euler didn't even discover this.
@@felixansell3901 It is called Euler's identity. The one you mentioned is the Euler's formula.Things are not always named after their discoverers. Eg. the pythagoras constant(root 2) was discovered by Hippassus(the spelling may be incorrect) but it is named after pythagoras as it is derived from the pythagoras formula.
man, this channel really deserves more awards. I know its won awards before but they need to make more awards so they can win them
Boy did I love this and I was able to follow it almost to the very end. Thank you for making me feel smart and remember dont drink and derive!
Psy trance djs sampling this episode for sure . "E is transcendental " lol
"its a time when you're really into... Out I'd body experiences and stuff" Psychedelics. He was trying to not say psychedelics. Lol
Othership Adventures you already know all these mathematicians are hipped
6:09 Dude, learning that it was a number cost me a lot of debt. You just explained it better in like 15 seconds. Thanks mate.
Absolutely Mind Blowing! I appreciate Complex AKA Imaginary Numbers so much more! Your Passion makes me Exhilarated! So much Fun learning from You!
"10 equals 10 in base 10." Hilarious on so many levels!
The way you did it still works, but I like to combine roots. So the 2√2√3, I would make into 2√6 and then square that.
Once you've seen this a few times the concept really starts to make sense!
Love this guy's enthusiasm!
Great moves, Ethan.
Great explanation. It's much entertaining than watching any movie.
Could be my favourite numberphile vid!! love it.
Brilliantly clear. Thanks. Very very enjoyable!!
8:56 Captions: [INAUDIBLE] should be “cooler”
so much passion :) you guys are amazing.
Thank you for this elegant explanation.
You can tell Simon was holding himself back from jumping up n down at how excited he was getting.
The audio captions have [INAUDIBLE] at: 8:54 "there's actually cooler stuff I can show you other than e."
"No flies on you mate", what a great compliment :D
It's wild to think how much power the contradiction "a is a whole number between 0 and 1" has. I feel like now that I'm getting into more advanced maths and proofs, it pops up all the time when it comes to proving that something is irrational, or transcendental, or any number of things.
This is perhaps the best numberphile video
Interesting discussion. I've always thought simply of transcendental functions, but never considered a transcendental NUMBER as being an actual singular number that is not a root of some characteristic polynomial equation.
I agree..
How to beat the magician: Magician: "Pick a number." Nobody: Me: "e"
His excitement is infectious
My initial comment would have been, "The only thing this video taught me is that Pi=22/7": sarcastic appreciation. But this man's clear dedication to his craft makes it impossible for me to mock, even unintentionally. I've enjoyed many of your videos, but this one touches a nerve I never even knew existed. And I thank you for that.
What I find even more surprising is how few algebraic numbers there are. There's an infinite number, sure, but it's only _countable_ infinity. Which means that there are as many algebraic numbers as there are natural numbers and that's just fantastic.
Wrong, there are uncountably many algebraic numbers because there are irrational algebraic numbers
+Cubi Cadi - That's like saying "there are uncountably many natural numbers because some natural numbers are real". It shows a fundamental misunderstanding of logic.
@@Nixitur isn’t what @Cubi Cardi is saying more like “there are uncountably many real numbers because real numbers contain irrational numbers, which are uncountable”? Because algebraic numbers contain some of the irrational numbers
@@muhammedkoroglu6544 No, they are literally saying "there are uncountably many algebraic numbers" which is objectively false.
@@cubicardi8011 the algebraic numbers are a countably infinite union of countable sets, which is countable
if e to the power any algebraic number is transcendental , it would mean that ln2 , ln3 .i.e natural logarithms of all algebraic numbers are transcendental . Because if they weren't e to the power that number would be algebraic , which can't be!
Surely this should read "if they weren't, e to the power that number would be *_transcendental,_* which can't be?"
ln2 isn't algebraic is it?
Very nice explanation of what algebraic numbers are.
I was definitely into out of body experiences during my first round at uni!
Have you ever made a video about Euler-Mascheronni constant? Also known as Napier's constant or number e?? I believe a lot of people already know but a lot don't and the history behind it must be quite interesting, so many mathematicians behind and using it… An intro for logs, natural log, calculus… I know that the function (1+1/n)ˆn; if n gets arbitrarily big, it tends to e Where else can the number appear??
I see that in this videos thumbnail you have pi tetration e. I'm sure this wasn't on purpose, but it leads me into the following request. Could you do a video on what comes after exponents? Aka tetration. Or a video describing all the hyperoperations? Hyperoperation 1 is addition hyperoperation 2 is multiplication hyperoperation 3 is exponents, hyperoperation 4 is tetration, and so on.
I thought the subscript meant base; as in: e in base π. They should redo their dungeon number -video with tetration, instead of bases. That would really blow up fast. Maybe something close to f_ω(n). 🤔
thank you for this video. you explained it quite well
this guy is my favourite in numberphile
e is a number? I was droppin' numbers in the 90's too some banging tunes!
The 90s were pretty great. I still eat lots of e tho.
until now didn't know that 22/7 is just an approximation of pi... thanks..!
Funniest and most energetic professor in this channel 👍
excellent material, thank you!
"you cannot not like pi" *Vi Hart enters the chat*
during this video I randomly looked at the clocked and it was 3:14 am totally unintended .0.
Excellent teacher, thanks!
Thanks for the new insight into the nature of transcendental numbers. Are you aware of how e is used in ontological mathematics?
6:52 "Hey let's mess with the subtitler. I'll write 24, but say 20. Won't that be a laugh?"
Is there a mathematical equation that proves that pi is delicious?
***** Nice.
***** False premise, whole numbers are rational numbers, and I always like to eat the whole thing. Also, pi has nothing to do with pie, so again, false premise. Also, tau is the one true circle constant. All hail the hypno tau.
***** XD
If seven 8 nine, does that make seven a cannibal? And what does 69 taste like?
LanceAtlas Uh, hate to break it to you, but Pi radians is only half a circle. If you want to eat the whole pie, you're going to need Tau.
I like that way of thinking about the square root as a sentence. Now for some reason roots are a clearer concept to me.
love this dude!
11:09 ooooohhhhhhh Mathematician roasting engineer
13:10 Checkmate!
What do you mean?
Jack Sainthill Im just commenting on the finality of his delivery. Probably sounded funnier in my head than it did in text.
Rather, the point was more _obvious_ in your head than it was in other people's, perhaps. Anyway, I've plussed it, albeit only because of your boldness in granting the community the intelligence to work it out for itself - an excellent comedic device when it can be brought off, but which is also, alas,very difficult to judge properly.
I found this channel very late! Evey video is fantastic!
I fucking love this channel. I really do. I look forward to these after work now. Keep 'em coming guys.
Leave it to a mathematician to confirm base 10.
As a non-mathematician, I too love pie (9:42), meat pie, shepherds' pie, apple pie ...
Cottage pie, mince pie, chicken pie, fish pie...
This ripped the top of my head off.
I loved this one.
2:50 He's *irrationally* happy.
LOL
I laughed at this lol, but isn’t that what beauty is? What’s beautiful in substanceless ratios
Can anybody answer this for me. can't you just take pi to the power of 0, and then subtract 1? Heck, why cant you just multiply pi by 0. that fits the rules of the game showing that it's an algebraic number. This must be wrong, but i cant see why.
It makes the game too easy
How to make π: To make the dough for the pie crust, mix 2 1/2 cups all-purpose flour and 1 teaspoon each salt and sugar in a medium-size bowl. Cut 2 sticks chilled unsalted butter into pieces. With a pastry blender, cut in butter, working until mixture resembles coarse meal. 2. Add 4 tablespoons ice water; work with hands until dough comes together. If dough is still crumbly, add more ice water a tablespoon at a time (up to 4 more tablespoons). Do not overwork. 3. Divide dough in half, and flatten halves into disks. Wrap disks separately in plastic; refrigerate at least 1 hour. 4. To form the pie shell, roll the dough on a floured surface into a 14-inch round. Wrap around rolling pin and carefully unroll over a 9-inch pie plate. 5. Fit gently into bottom and side of plate. Use kitchen shears to trim dough to a 1-inch overhang; fold under, and seal to form a rim. 6. Crimp rim with fingertips and knuckle. Repeat with remaining dough; wrap each with plastic, stack, and freeze.
That look of disappointment when he heard ten as the favorite number, he just had to double check "10 in base 10?" "Yeah" "Okay peasant"
Who knew h3h3 was such a maths genius?
Vapenation yall \//\
?
Olivia Lambert *math
Olivia Lambert *math
+Jacob P *maths
10:10 according to that, 0 is not an algebraic number :D just nitpicking
I love this video so godamn much
At 10:16 simon says the "e raise to any algebraic number is transcendental ..but he forgot to say that the number also needs to be non zero , since e^0 is 1 which is not transcendental
Is the following expression correct?, e^(1-1)-1=0. (I am using only the functions that you listed) if so, how is e transcendental? Please clarify.
It's trivial, and you could do that with any number excepting zero.
(1-1) isn't a whole number coefficient. 1-1 is zero, which is not usually considered a whole number. Also, you can multiply any number by 0 and get 0, transcendental numbers included. It's kind of the math equivalent of defining a word using the word you're trying to define. An algebraic number needs to reduce to zero using a rational polynomial that isn't zero.
Well, he was lying, you can only take something to the power of a natural number. x to the zeroth is not allowed.
"you can not not like pi" *writes down Tau :D
I love these guys
Euler's identity is still the most beautiful thing I've ever seen in my life.