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65 results
f : S n → R n {\displaystyle f:S^{n}\to \mathbb {R} ^{n}} is continuous then there exists an.
33 views
5 years ago
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks ...
3,037,013 views
6 years ago
Compactness is one of the most important concepts in Topology and Analysis, but it can feel a little mysterious and also contrived ...
375,465 views
10 months ago
We discuss the Borsuk-Ulam theorem concerning a continuous map from the sphere to the plane, and the Ham Sandwich ...
12,392 views
12 years ago
One technical note: It's possible to have fractals with an integer dimension. The example to have in mind is some *very* rough ...
3,949,688 views
7 years ago
Timestamps: 0:00 - The size of the monster 0:50 - What is a group? 7:06 - What is an abstract group? 13:27 - Classifying groups ...
3,008,678 views
3 years ago
Timestamps: 0:00 - Intro 4:14 - Linus the linelander 11:03 - Felix the flatlander 17:25 - Mapping 4d to 3d 23:18 - The geometry of ...
4,616,741 views
Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are made ...
5,153,918 views
4 years ago
Timestamps: 0:00 - Car example 8:20 - Areas under graphs 11:18 - Fundamental theorem of calculus 16:20 - Recap 17:45 ...
2,259,619 views
I had a lot of fun chatting with Grant Sanderson (who runs the excellent 3Blue1Brown YouTube channel) about: - Whether ...
300,655 views
8 months ago
Artwork by Kurt Burns Music by Vince Rubinetti Nice writeup and video giving solutions to the exercises at the end, by Benjamin ...
1,892,186 views
2 years ago
This is my submission to 3Blue1Brown's "Summer of Math Exposition 1" #SoME1. In this video, I explain what Dirac's famous belt ...
414,210 views
In the video, I referenced our own blog post expanding on this argument. Unfortunately, it managed to get lost during a website ...
812,059 views
There's a small error at 19:30, I say "Divide the total by 1/2", but of course meant to say "Multiply..." Curious why a sphere's surface ...
2,694,848 views
0:00 - Intro quiz 2:24 - Discrete case, diagonal slices 6:49 - Discrete case, flip-and-slide 8:41 - The discrete formula 10:58 ...
650,882 views
11 months ago
We define the degree of a function from the circle to the circle, and use that to show that there is no retraction from the disk to the ...
13,444 views
Timestamps 0:00 - Introduction 1:39 - Counting lattice points 5:47 - Gaussian integers 10:30 - The lattice point recipe 17:50 ...
2,536,233 views
We define the dual of a polygon in the plane with respect to a fixed origin and unit circle. This duality is related to the notion of the ...
14,563 views
This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the ...
3,430,326 views
Not on the "homework" to show that exp(x + y) = exp(x) * exp(y). This gets a little more intricate if you start asking seriously about ...
1,208,465 views
Streamed 4 years ago