Відео

My favourite: 6:18 120-Cell Dot -> line ‐> pentagon ‐> dodecahedron

Pál is his given name (not family name). Pronounced like Paul

the forest problem makes 0 fucking sense to me how is every answer not just a straight line

I think that "octochoron" sounds cooler then "teseeract". Altough, i think that polychoron means only the 3d surface of the hypersolid, for example octochoron means only the 8 cubes, not the inside. Its like a cube is the entire shape, but hexahedron is only the surface

Do you use ai for your voiceovers?

clickbait title, not every shape is covered, as that would take an uncountably infinite number of hours

Great video. I think you could have left some of the example pictures on the screen for a few more seconds to give us time to see them. I had to rewind and pause a few times.

How is a tesseract "complex geometry"? Its a hypercube, one of the most basic families of polytopes.

"Fractal Dimension" spits in the face of what a dimension actually is, and then it holds its mouth open and pisses in the mouth of what a dimension actually is, and then it .... Dimensionality has nothing to with a shape's area. The correlation between the side lengths of hypercubes and their areas is a coincidence, it certainly does not define what a dimension is. If it can exist within a linear world, no perpendiculars, then it's 1-dimensional. If it can exist in a flat plane, nothing perpendicular to a plane, no matter what shape it is it is 2-dimensional. The sierpenski triangle is 2D.

Why don't just made up new number system?

Surface of Revolution would be an awesome band name.

I have been tinkering with the tesseract a bit: Take a 4x4 chess board and stretch and join it to form a torus. Then the squares of the chess board correspond to the vertices of a tesseract, with the edges corresponding to knight moves. Then allocate 4 digit binary strings to each vertex according to the 4 coordinates of each vertex of the hypercube. The flattened out chess board then becomes a magic square, with each row, column, major diagonal and 2x2 square having sum 30. Regular 4 digit Gray code gives you a nice symmetrical vertex traversal of the tesseract, whereas for an edge traversal you can use balanced Gray code.

LiaF reminded me of a similar problem. I saw a problem about a spaceship. I didn't solve it, but I thought of a similar problem in 2D. In LiaF terms, the forest is a half of a plane, but you know you're at the distance a from the boundary. I then changes to a different problem, found a solution for it and translated it to the 2D version of the original problem. Then, someone else came up with another solution. I successfully translated it to the different problem. It could prove that my solution was more optimal, but the calculations said otherwise

It's ridiculous that mathematics is considered a serious study. This stuff is just "Everything I say is a lie" with numbers.

line ,"volume"=s square "volume"=s^2=s squared cube volume=s^3=s cubed logic: tesseract HYPERVOLUME=s^4=s tesseracted

ENTROPY? MEASURE OF DISORDER? Completely incorrect, entropy has nothing to do with order. Entropy is related to the number of possible micro states, which increases in the path to equilibrium.

Fun fact the Sierpinski Triangle, and also the similarly constructed 3D shape the Menger Sponge, technically have no area/volume.

How can you miss Gauss?

Ugh, I'm too stupid to understand what any of these are getting at.

Sierpiński Triforce

tRiNglE!!! 5:14

Moser's worm completely flies over my head. I don't even understand the problem. I don't think this should be in a video about things that sound easy 😅

I think I'm missing something about Lesbegue's universal covering problem: wouldn't the shape with a diameter of 1 that has the smallest area simply be a line with a length of one and no width?

Replace the battery in your smoke alarm. 11:10.

Every?

lol, couldn't give two s**t's about maths but these are still pretty interesting

I learned something

I watch a lot of your videos and still don't understand any of them.

Nice. Dimensional analogy is a very handy tool in this topic.

How can an infinite hotel even be full in the first place?

You're the best, thanks!

The Hypersphere and Hyperball section made my brain explode with a lack of understanding.

Hi! Your video is very good! Keep it up!

Man I loved this video, but I’ll be honest the brutal inaccuracy and inconsistency of the lines in the square packing problem was very unsatisfying. The lines didn’t touch in places the should have, uneven gaps, different thicknesses etc

i fell asleep while looking for a video

I don't get, why there is a discussion about the vase and balls "paradox". You always put in more balls than you take out => you never will have 0 balls in there. It doesn't matter if you remove countable balls, when you always add more than you substract.

St. Petersburg isn't a paradox. Time is the main reason why people don't play the game. You need to accumulate a lot of plays/time to get a decent profit. With that amount of time you can make much more from other investment

these makes no sense. Just a bunch of wording technicality

"We can't figure out Pi+E." "Pie."

Dart board? 1/infinity? You’re just dividing by zero

The lamp reaches planktime and at that point you can’t go any faster

Lesbegue's covering problem: why not cover with a circle?

Ulam's packing conjecture: what about half a sphere? What about half a sphere glued to a slice of a larger sphere?

I have some nit-picky criticism 1. The standard definition of a vector is a bit questionable, since direction doesn't really mean anything if you think about it. You can define angle though, which is more meaningful, but the axioms of vectors only require addition and scaling. 2. Your explanation of the dot product implies that it would always be positive; this is not the case. 3. I wouldn't say the wedge product is exclusive to geometric algebra, it was around way before this, and a necessary tool in representation theory, just as the general tensor product. But it is completely true that this is the correct version of the cross product! Down with the cross product! Up with the wedge!

Ok, I am not that great at math and many concepts in this video confused me, but for Ross-Littlewood paradox, wouldn't the answer be n×9, since you put in 10 balls and then remove 1, so at the end of the turn there are only 9 balls left in the vase so 1x9=9, 2×9=18 and so on... In other words, wouldn't the paradox be that you end up trying to fit infinity×9 into 1 infinity thus creating separate paradox of statement that is impossible and possible at the same time?

The lamp will be off, because your dad yelled at you.

Unsurprisingly, “Littlewood” spent his immense leisure time pondering sums that don’t exist

You talk about the dartboard as if the tip of the dart was infinitely small as well, but the dart does take up space. The dart can hit multiple infinitely small points on the board at the same time. If you measure the surface area of the dart (D = Dart = N1) and the surface area of the board (B = Board = N2) then you will have a N1 in N2 chance of hitting any given spot. It’s an interesting theory though. If the dart tip was infinitely small and the very tip was the only part that would ever hit the board, it would be very cool to think about.

The explanations of fractals like the Serinsky Triangle and the concept of fractal dimension blew my mind. It's amazing how mathematics can turn seemingly simple objects into something so intricate and beautiful, especially with fractals like the Mandelbrot set. Awesome content!

Concerning the dartboard, I'd say the probability that the dart hits a specific point is not 0. But since the point is infinitely small, so is the chance to hit it. So the probability is not 0, but it approaches 0. Boom, no more paradox.