Ngl I wasn’t wondering that, but nice video.

Dr. Peyam in New York. Man: Sir, can you tell me how to get to Broadway? Dr. P: I'm glad you asked! (Pulls out whiteboard.)

@blackpenredpen

3 жыл бұрын

😂

@drpeyam

3 жыл бұрын

Hahahaha

Protip: always try to prove/derive the topic on your own before watching the video

So, just to check I haven't fallen asleep while my compile was running, the "d2 sphere" is actually an octohedron, right? I'm intrigued what happens in higher dimensions, when most of the Platonic Solids drop out.

@iabervon

3 жыл бұрын

The balls for d1 and d-infinity are two of the three that don't drop out.

Je me rappelle quand mon prof de maths nous a montré ça, je devais avoir 16 ans ... Ce cercle carré m'a souvent empêché de dormir parce-que je me disais que si je mesurais la distance au centre avec une règle, le rayon ne serait pas constant. Erreur ! Tout c'est arrangé lorsque j'ai compris qu'en fait la règle et ses graduations subissaient la même déformation, et donc que le rayon était bien constant. Il suffit d'imaginer que l'on voit le monde avec des lunettes spéciales, qui ont des verres déformants (pyramidaux ?), et tout redevient normal, il n'y a aucune incohérence. Ça m'a fortement marqué, c'était il y a 50 ans et je m'en souviens encore. Le mauvais côté des choses, c'est que maintenant je ne comprends plus ce qu'est une ligne droite, mais ça c'est une autre histoire :-D

@drpeyam

4 жыл бұрын

Incroyable, non? 😍

beep bop, R2D2 0:18

It helps me a lot understand how normed vector space works! Thanks!

@drpeyam

3 жыл бұрын

You’re welcome :)

Thank you! I told my wife I was going to the shop to make some square discs and she said they didn't exist. I made some square discs and she still called them squares. I will have to show her the video.

@drpeyam

Жыл бұрын

Hahahaha

So we're squaring the circle? I'm listening! :D

i was wondering that!!

VOCÊ É BOM PARA UM CARALEO! TRANSLATE FOR YOU: YOU ARE AWESOME BRO! YOU REALLY MAKES ME UNDERSTAND! AND NOW I AM THINKING THAT'S COOL! REALLY THANK YOU, YOU HONOR THE TITLE OF DR!

R2 d2 oohhhhh that's where the name came from.

I don't understand how, at 6:23, the |y|

@notu483

Жыл бұрын

Okay, you changed to exclusion. Nevermind.

Wow this is super cool. I had never of even thought of this neat application of metric spaces. I guess a "Ball" is not what you think it is! Blew my mind. Btw, I was smiling the whole time while watching the video :)

Ha ha ... I like it! Transformer ball!

A squircle. Start with a circle X^2 + y^2=1, then let exponent n, a whole number, approach infinity, x^n + y^n = 1, and the circle morphs into a square. *even whole number.

Made a funky pattern in desmos based on this bphunumor8

@drpeyam

3 жыл бұрын

I love this, thanks!!!!

Are these metrics different from norms? They seem to be named and work in a very similar way to the 1-, 2-, and infinity norms of vectors. This would give the n-norm of a vector in Rk as (Sigma(j=1tok)|y_j-x_j|^n)^(1/n), and we go from the, slanted square/octahedron to circle/sphere to more and more square-like smooth shapes until we get the 2x2 square of the infinity norm.

@pesilaratnayake162

3 жыл бұрын

I guess, which are more general? Norms or metrics? Or are they identical?

@drpeyam

3 жыл бұрын

Metrics are more general

@drpeyam

3 жыл бұрын

If you have a norm then d(x,y) = ||x-y|| is a metric, but for some spaces (like Example 9) there is no norm

It feels awkward that the points are (X1,X2) and (Y1,Y2) rather than (X1,Y1) and (X2,Y2). Usually X and Y are coordinates rather than names of points. Awkward or mind-expanding...

@drpeyam

3 жыл бұрын

I agree, it’s the stupid convention of the textbook, drove me nuts for the whole chapter

@nathanisbored

3 жыл бұрын

@@drpeyam P and Q or something would have been better i think

What about a metric like D = |x-y| + |x+y| That should also give you a square.

@scose

3 жыл бұрын

Not zero when x = y

@quantumsoul3495

3 жыл бұрын

@@scose Does that mean it's not a metric ?

@scose

3 жыл бұрын

@@quantumsoul3495 yes

@MagicGonads

3 жыл бұрын

​@@scose here this is referring to the x,y coordinates of the second point so D((x1,y1),(x2,y2)) = |x2-x1-y2+y1| + |x2-x1+y2-x1| (x1,y1) = (x2,y2) => D(...) = |0-0| + |0+0| = 0

Slippery slope to proving flat earth.

You are damn cute man!!!!

You didn't answer the question 💔

@drpeyam

3 жыл бұрын

Yes I did! A disk can be a square with the appropriate metric

@CC-nf6or

Жыл бұрын

Thank you! I told my wife I was going to the shop to make some square discs and she said they didn't exist. I made some square discs and she still called them squares. I will have to show her the video.