How in the world? Pi and e are like church steeples in an old European town that keep unexpectedly revealing themselves when you round a corner. And Pascal's Triangle is rife with churches and innumerable other surprises. Many thanks! (p.s. plus sign at 7:13 was a trivial mistake)
Not especially surprising -- given that there's a RUclips video about it, it was either going to be e, pi, or phi, right? And we know that factorials can be rewritten in terms of e using the gamma function. I wonder if you could have done it that way!
9:08 think he says THIS wrong as "future over present and present over past" - if so presents cancel out then it's future over past BUT board shows future over present and past over present - BOARD LOOKS CORRECT THOUGH! Edit: i may have misheard him but again board looks correct - "future over present *divided by* present over past" my initial comment suggests he was multiplying instead of dividing which incorrectly leads to cancellation i mentioned previously.
Surprising things happen at infinity. I still can’t wrap my mind around the fact that the sum or product of rational numbers can become irrational at infinity.
@@micknamens8659 Nah. Most of his posts are way above my grasp (and I am an old man), let alone a child's. Recently I did watch another interesting post of his, till the point where he mentioned his 'partner'. That ruined it for me.
Very well presented. Who would have ever thought. Thanks Dr. P.
Thank you so much for the suggestion :)
e is that one kid in high school who knows literally everyone
Pi is his older friend
I like this a lot. However, It's not really that surprising if you recognise that (1 + 1/n)^n is simply a binomal.
This is very unexpectedly cool!
I didn't think the factorials would all cancel out (I thought we would have needed Stirling's formula)
How in the world? Pi and e are like church steeples in an old European town that keep unexpectedly revealing themselves when you round a corner. And Pascal's Triangle is rife with churches and innumerable other surprises. Many thanks! (p.s. plus sign at 7:13 was a trivial mistake)
Taught about it by Sir Rana in 1999 in our 11th grade in Quaid-i-Azam College, Chaklala, Rawalpindi, Pakistan. 🥰
Love the result! Also liked the enthusiasm! Good vid!
Unexpected indeed! Next challenge, pi from pascal triangle ... ☺
Newton did it
I was just thinking about pascal identity and it’s connection with pascal triangle , thanks for the vid you’re great
Thank you for sharing this.
With luck dear Dr, Hoping for more videos.
Awesome! What did motivate you to examine that limit?
Very fascinating the result!
Not especially surprising -- given that there's a RUclips video about it, it was either going to be e, pi, or phi, right? And we know that factorials can be rewritten in terms of e using the gamma function. I wonder if you could have done it that way!
Grand finale is BEAUTIFUL!!!!
9:08 think he says THIS wrong as "future over present and present over past" - if so presents cancel out then it's future over past BUT board shows future over present and past over present - BOARD LOOKS CORRECT THOUGH!
Edit: i may have misheard him but again board looks correct - "future over present *divided by* present over past" my initial comment suggests he was multiplying instead of dividing which incorrectly leads to cancellation i mentioned previously.
This was great. A very unexpected surprise for me as well.
Surprising things happen at infinity. I still can’t wrap my mind around the fact that the sum or product of rational numbers can become irrational at infinity.
I would, because of the factorial nature of the entries.
That's a cracking result, indeed!
Well, I expected it from the low N value 64/27, but the proof was cool!
Oh my God! And now what about the sum of the futur to the sum of the present or to the past??
Great video but the thumbnail spoils the surprise 😂
Il capo di tutti li capi!
Where do you find this crazy stuff Peyam !
Very Excellent 👍👍
Thanks! 😊
Very nice!🌞
You're awesome!
Thank youuuu!!! 😊
@@drpeyam 😊
where did you find this? WOW
Fenómeno
How???? How is this possible???? Great discovery!
Nice 😊
Thanks 😊
My favorit: 0 choose x = sinc(x) = sin(pi * x)/(pi * x) => 1 choose x = sinc(x) + sinc (x - 1) and so on.
❤❤❤❤❤ that's really amazing
Everything else is hidden in Pascal's triangle, why not e? :D
Gosto de suas camisas.
Why is it (N+1)^(N+1) and not (N+1)^N? Because we are starting at zero?
yes
Hello from Indonesia Dr
دکتر پیام لطفا از قلم های ضخیم تر با نور بیشتر استفاده کنید، من این قسمت را خیلی دوست داشتم، ممنون
I loved it…
Thank you!!!!
The only thing that was abnormal to me in the video was him being lefty. But yeah.
The baby is the sum of the parents....
Thats not a family tree i want to be a part of.
technically kids are the average of their parents 🤓
Where did you find this? I’ve never seen this before
It was recommended by Ian Fowler, a wonderful subscriber of mine 😊
🤯
*It wasn't surprising because the answer was literally in the thumbnail*
OwO! Very very! It's very, very surprising!
(Sigh, checks wikipedia)
Love the content, the erudition and the refreshing, child-like enthusiasm, but why act so effiminate?
I guess his target audience are children, so he has to entertain them.
@@micknamens8659 Nah.
Most of his posts are way above my grasp (and I am an old man), let alone a child's.
Recently I did watch another interesting post of his, till the point where he mentioned his 'partner'. That ruined it for me.
The notation is discusting
I think e should be worshipped
Man, math seems to be funny for you.
I think math drives people to be madmen 😅
All that remains is to show lim(1 + 1/N)^N = e.