Comments by "Christian Baune" (@programaths) on "3Blue1Brown" channel.

  1. Forty Two.
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  2. You can also see that as a sequence. For example: square, increment, double You can imagine it's a factory line and you could "square and increment" then "double": 3->10->20 You can also "square" then "increment and double" 3->9->20 It's just that you did put one different part of the production line in a big box, but ultimately, you are still doing the same processing in the same order. So, it's associative!
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  3. LOOOL, 1 week after I had to write a course on this 🤣
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  4. I did a presentation showing how isomorphisms are very useful to solve problems because you can end up with an easier model or an already solved problem. What you keep by doing this is also an invariant: intrinsic properties. One example is: can you order a list of 3 digits binary numbers so you start with 000 and end with 111 by changing only one digit from one number to the next ? This is similar to finding a path between two opposite vertex of a cube, which is much less challenging. If you try the same with 4 digits binary numbers (0000 to 1111), you end up doing this on a tesseract that you can flatten as a simple graph or two connected cubes. Showing $$\sum C(2,n) = n^2 $$ can be done by seeing that binary numbers can represent all the combinations in a set. As an example 101 means: pick first, discard second, pick third. Of course, when you are presented with these morphisms, you think "Yeah, that's stupid.". It's not. Here is a nice problem that can be solved in that particular way: We create a 4 by 6 grid of vertices, how many rectangles can be drawn by connecting 4 vertices with horizontal and vertical segments ? Can you give a general solution for a m by n grid ? Extension (that requires one to use the elegant solution): we create a 20 by 20 grid of vertices. We can identify each smallest possible square by it's row rank and column rank. We draw a dot in the square at 7,10. How many rectangles can be drawn by connecting 4 vertices with horizontal and vertical segments and enclose the dot ?
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  5. Here is mine: https://www.programaths.be/games/covid19/ You have to resize the window to make the walking area smaller.
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  6. It's a polarizing video with a lot of twist. At least, we saw the light.
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