The Dark Side of Pascal's Triangle #SoME4
22K views · Feb 20, 2026 · Education
Comments · 51
@mr.winter538 · 6 months ago
To anyone interested: There is another idea like this. It is called a Laplace Transform and actually does more or less what we have been doing here and does it again with a generalization of the Fourier Transform. It also turns calculus into algebra. In that case we use (possibly complex) exponential functions instead of polynomials to get a new kind of basis. It's very cool!
8
@deet0109mapping · 7 months ago
Ever since I heard of Pascal’s triangle as a kid, I wondered if you could extend it to the negatives. Thanks so much for making this video.
3
@rusticmouse · 7 months ago
I know that I have seen the original video, because my teacher talked about Pascal's triangle and I got reminded of this video.
11
@rubyjemstar · 7 months ago (edited)
Re-upload ?
97
@alexandersanchez9138 · 7 months ago
Very nice. Piano intro is from the ending of Kapustin's Concert Etude 3.
7
@PawelS_77 · 7 months ago
This reminds me of another thing that has a "dark side" alternating between positive and negative: the Fibonacci sequence.
38
@147JMP · 6 months ago
Umbral calculus is cool. I remember getting the Gregory Newton formula and comparing it to Taylor series. Then I said let’s define a general forward difference operator like this: f(x+h)-f(x)/h <br>Then I got the general Gregory Newton formula to be the same as h=1 except now it’s x/h instead of x. It would be interesting to see things on eigenfunctions as well. For example h=3 means the eigenfunction is some scalar multiple of sqrt(a)^x<br><br>I also struggle to find things on umbral calculus so more videos on this would be awesome!
2
@R0mm3n · 7 months ago
Still love this video!! :D
9
@DeerDesigner · 7 months ago
<a href="https://www.youtube.com/watch?v=xP8Z7IgIIZs&t=79">1:19</a> chess battle advanced
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@mabegamingchanel4218 · 7 months ago
Great video, thank yo for effort putted into it!
1
@tony148brown · 7 months ago
Still waiting for the dark side of stirling’s triangle…
9
@퀴라지 · 6 months ago
4장부터 흥미롭네
1
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