Very clear expelation.

11:19 it is usually written as omega*2 rather than 2*omega because of its multiplication definition.

From Mathemaniac as well. Great video! If we alter the rule from "twice" to "three times", will we be dealing with another sequence?

That's very good explanation. Thank you:)

Hello, I'm from Mathemaniac, gonna recommend the channel to my students :)

13:44 can't you just remove 13?

here from Mathemaniac! this is really awesome

The other (nim) cube-roots of 2 are ω⊗2 and ω⊗3, because exponentiation distributes from the right on multiplication, just as we'd expect . And you gave the hint that 1, 2 and 3 are all cube-roots of 1 :)

are there any assisting arcs to help manual tiling of spectre tiles like those on penrose kite and darts? in this video at 10:06 (anyhow, the video begins with the same decorated tiles.) kzbin.info/www/bejne/amnWdKtjrKemaZY

E' spiegato benissimo!

Pure Gold!

beautiful ❤

If monotiles cannot exist in 3d (which we do not know yet), I don't think the same would apply to 4d or any other nD where n=x^2, but I have no reason to believe this other than intuition

Great video

if zero is the empty set, {}, and the constructor for Surreals starts off by dividing two empty sets, {|}, then the construction of the Surreals in fact only ever generates different names for zero: {} = 0 {|} = {{}|{}} = 0 {0|} = 1 = {{}|{}} = 0 {1|} = 2 = {{}|{}} = 0 {0|1} = 1/2 = {{}|{}} = 0 and no matter what you do, this is how every 'surreal' is constructed. which means you're an idiot.

Who is the guy on the Mostly Mental videos on KZbin? I learned great gobs of stuff from his video on the Spectre tile. I would love to be able to email him, and bounce some ideas around with him. He introduces himself on his videos as Foxy or Doxy or something like that.

Ces formes je les ai decouvert en 2013

You should write a book. I’d buy so many copies so I could have one at all times

can you provide the proof that the sprague grundy value of a position in the game of twins is the nim sum of the sizes of piles

how did you define the length rad3?

Great explanation. In our remodeling we were considering using Penrose tiles. Then the hat and soon after spectre were discovered, now we are looking for a tile maker who'd make this for us.

I found this very interesting and you explained it very clearly. Thanks for making this video.

Yay! You're back!! I'm always excited to see your videos, friend :) Nim and game-theoretic extensions of number systems (like what Conway and Knuth developed) are truly an underappreciated love of mine. Thank goodness you have Aurora as your assistant!!

I would like to see a video about Chomp

9:15 proof If f_n is the highest fib which goes into some number, then [f_(n-1)]+ [f_(n-3)] + [f_(n-5)] ... + [1] is the largest number we can construct without using f_n and following the rules. we can expand each term[f_(n-2) + f_(n-3)]+ [f_(n-4) + f_(n-5)] + [f_(n-6) + f_(n-7)]... + [1 + 0 ] . This sequence is the sum of the first n-2 terms and it sums to f_(n) - 1 . (easy to show via induction.. f_1 + f_2 + f_3 = f_5 - 1, therefore f_1 + f_2 + f_3 + f_4= f_5 + f_4 - 1 = f_6 - 1) So the biggest number we can create without f_n is less than f_n and therefore less than the number we are trying to sum to. This means f_n must be used in our representation. then we can use the same process to deduce that in order to reach (our target - f_n) we must add the largest fib which fits into (our target - f_n). So in order to get a valid representation, we're going to get a single list of numbers we must use, therefore unique.

Great explanation! Glad you're back!

Aurora seems like a good sport!

You know another thing that's also mental, only completely so, it's the topological inversion of a sphere inside out...

cool facts about hyperbolic geometry: almost every path is close to straight equidistants (paths that stay the same distance from lines) converge to a horocycle (circle of infinite radius) as the guiding line goes away

is there a link to that game ? what great visual add. thanks for the vid

i love your channel!!!!!!!! please don't stop making videos, they're great and i love learning math without the pressure of exams!

Good explanation, simple approach. Nice!

Just turned in. Find it strange to be ending on hackenbush so I’m curious where you started

Does one orbit refer to one shell/one layer of the sphere? This video is the perfect blend of maintaining the technicality of the concept along with making it easy for the viewers. Thank you so much for such a wonderful video.

I highlighted the need to see this video on the Wikiversity article "Surreal number" and will attempt to include a link to this video on the Wikipedia article with the same name. Nothing on any of these wikis come close to explaining surreal numbers this well.

Amazing video!

How to measure the curve of the road ?

sick bikies

Nice

thanks for the explanation of crossing paths I was struggling with it.

Good series! Too bad it seems to have been discontinued(?).

Sir, will you provide the reference book please?

By the way, keep Going! You are incredibly gifted at explaining complex ideas 🫂🛐⚡

One thing that strikes me here if I am understanding it correctly is that you have this kind of spectrum in which the hat side consists of a continuum of hats between chevron and spectre and the turtle side consists of a continuum of turtles between spectre and comet with all these intermediary tiles having the property of tiling the plane only in an aperiodic fashion but involving a certain number of reflected versions (proportion phi to the fourth power) with the spectre in the middle which can be tiled periodically or periodically but which heads a family of spectre mutants having chiral figures taking the place of its non-chiral line segments. This infinite family of spectre mutants has the property of tiling the plane only periodically. Cool!

I’m having to pick some of this up for research, great video!

hello

another question, do you know where can i find something more specific about the "ein stein" problem that the hat broke? an article talking about this problem or something? thanks :)

hey, i would really appreciate if you could share your references for the aperiodic tiling with trapezoide tile demonstration, starting at 1:34. thank you!

I appreciated the series. Thank you kindly.

Please keep doing videos about this topic, i was looking for so long!! Thanks🎉🎉🎉