Transcendental Numbers - Numberphile 

"So it'll be 10$ sir." "You mean 10 in base 10?" -_-

My favorite part of these videos is how excited each mathematician gets about their particular number. Other people feel how I feel!

'7π - 22 = 0' - Simon Pampena, 2013

I love that he said in all seriousness that if he could add to the knowledge of pi, he would die a happy man

You know things got serious when you're asked which base you're expressing your numbers in. :D

Are we just gonna breeze past people dying because of the square root of 2?

Using a “reduce to zero game” to intuitively explain algebraic numbers is actually really smart!

“You mean 10 in base 10?” - cheekiest comment ever made on RU-vid.

That sigh at the end knowing that a good days maths has been done... :)

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:

"Square root of 2, you know, people died for this number" STORY TIME

Glad to see that Syrio Forel didn't die after all :)

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.

"You cannot not like pi." Say that to ViHart.

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.

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.

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.

I'm such a massive fan of how much this guy loves numbers.

"no flies on you" aweome phrase

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*

Holy crap, imagine if the transcendentalist Henry David Thoreau discovered these numbers.....

Almost 58 years old (5 days shy) and I have learned something. Thank you. I sincerely appreciate it!

9:45 "You love Pi. It comes" -Simon Pampena, 2013

Psy trance djs sampling this episode for sure . "E is transcendental " lol

Make a video on Euler's Identity!!

It's great to see someone get so excited time and time again. You seem to love what you're doing.

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!!

10 in base 10?

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.)

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!

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

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

"its a time when you're really into... Out I'd body experiences and stuff" Psychedelics. He was trying to not say psychedelics. Lol

There's something so charmingly intense about this man, even in the first two seconds of the video: "It's mind-blowing"

This guy's passion is contagious.

Huge fan of numberphiler and I like your style the most . Cheers mate.

_“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

"10 equals 10 in base 10." Hilarious on so many levels!

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 knows where to get professionally produced LSD.

Great moves, Ethan.

8:56 Captions: [INAUDIBLE] should be “cooler”

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!

Once you've seen this a few times the concept really starts to make sense!

e is a number? I was droppin' numbers in the 90's too some banging tunes!

"No flies on you mate", what a great compliment :D

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!

Great explanation. It's much entertaining than watching any movie.

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.

Could be my favourite numberphile vid!! love it.

You can tell Simon was holding himself back from jumping up n down at how excited he was getting.

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.

so much passion :) you guys are amazing.

His excitement is infectious

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.

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!

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.

Love this guy's enthusiasm!

Brilliantly clear. Thanks. Very very enjoyable!!

How to beat the magician: Magician: "Pick a number." Nobody: Me: "e"

The audio captions have [INAUDIBLE] at: 8:54 "there's actually cooler stuff I can show you other than e."

This is perhaps the best numberphile video

Funniest and most energetic professor in this channel 👍

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.

Leave it to a mathematician to confirm base 10.

Thank you for this elegant explanation.

I was definitely into out of body experiences during my first round at uni!

"you cannot not like pi" *Vi Hart enters the chat*

2:50 He's *irrationally* happy.

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"

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.

during this video I randomly looked at the clocked and it was 3:14 am totally unintended .0.

Is there a mathematical equation that proves that pi is delicious?

I fucking love this channel. I really do. I look forward to these after work now. Keep 'em coming guys.

this guy is my favourite in numberphile

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.

excellent material, thank you!

Very nice explanation of what algebraic numbers are.

6:52 "Hey let's mess with the subtitler. I'll write 24, but say 20. Won't that be a laugh?"

loved when he laughed about being "interested in out of body experience" in college. wink wink

Excellent teacher, thanks!

thank you for this video. you explained it quite well

11:09 ooooohhhhhhh Mathematician roasting engineer

13:10 Checkmate!

I found this channel very late! Evey video is fantastic!

As an engineer, I can confirm that pi is 22/7. I can count to 20, but only if I take my socks off. Engineering degrees don't contain any maths whatsoever because there is simply no way that a mathematical concept could be applied in any way to any engineering problem. And under no circumstances could I enjoy mathematics and, for example, watch RU-vid videos on the subject.

until now didn't know that 22/7 is just an approximation of pi... thanks..!

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.

I love these guys

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.

5:51 People *_DIED_* cuz of this number

This guy looks like Matthew Santoro with a wig.

Ah yes if you're an engineer, "pi is 22/7". Devastating.

I love this video so godamn much

"you can not not like pi" *writes down Tau :D

Who knew h3h3 was such a maths genius?

I love this guy.

love this dude!