Dihedral Groups Part 1

Dihedral groups are simple and important examples of finite groups.
They represent the symmetries of n sided polygons.
Whilst the cyclic groups represent only the rotational symmetries of n sided polygons, dihedral groups also include the reflection symmetries.

[@suzannebuskens9086]

You really can present this matter in a logic and understandable way. Now I understand what we are really doing, why and how to work with it. Thank you very much!!!!

[@brittanyamstad6953]

Nice job, dude! This is one of the clearest explanations of dihedral groups I've seen. Can't wait to watch some of your other videos.

[@stefanikondic3808]

THANK YOU!
These videos are soooo helpful.

[@dakotami]

I've been watching your videos for two years now and I LOVE them. I love how you explain things.Thank you so much.

[@samuelschmidgall2090]

you are a legend among men

[@joaquinbrandan8664]

18 minutes of pure love

[@baovoquoc6358]

Thanks very much.

[@ngolerex1665]

It's really really interesting, you deserve it.

[@gutzimmumdo4910]

so its the rotations in a sphere instead of a circle.

[@michelef406]

It's a creative way to view it but one would have to specify along which and how many axes you put the numbers. And that would boil down to find the axes of symmetry as shown in the video...Basically.

[@1468910]

The justification for closure is incorrect. A wheel might be set up whose only "maneuvers" are rotations, as in D4, plus flips along the vertical axis. In this case we don't have closure since those actions may be combined to produce other outcomes indirectly, e.g. a flip along the horizontal axis.

[@bonbonpony]

Yeah, this "real world manouver" gimmick is not really a proof at all. There's a lot of "real world manouvers" that don't make a group. For example, taking an object from one box to another box when there's only a finite amount of objects in that box: it's definitely a manouver, and it's definitely reversible (just take the object from box 2 and put it back into box 1 where it originated), but you can do it only a limited number of times and no more, which means that after than number of compositions it won't be able to compose anymore. Or if you decide that your "real world manouver" is to take that object ouf of box 1 and throw it into fire: this time it's not reversible (breaking the inverses requirement) despite it being a "real world manouver". So yeah, long story short, this way of proving it is flawed (if one could even call it a proof).

[@gutzimmumdo4910]

@@bonbonpony stop being a clown, he is not providing any formal proff he is just providing intuition, want proff? go and get the right set of axioms and derive it straight from there, go and make a book like russel did that no one will understand nor use to convey intuition on the books matter, in fact, as russel also did, u will need to do an "introduction to mathematical philosophy" equivalent (wich still would be dense af) to explain the consepts of such books containing such proffs and derivations in a less dense manner.
He is talking about the rotations in a sphere instead of a circle.

[@bonbonpony]

@@gutzimmumdo4910 You realize that mathematics is ALL ABOUT PROOFS? :q
So I'm not sure who's the real "clown" here.
You didn't even get what I was criticizing, so stop fanboying.

[@michelef406]

@@bonbonpony Math is about intuition first, and then trying to prove yourself right or wrong. The video is providing the first element in a very good way, if you want more rigor there are people on YT doing that as well.
You all need to stop turning everything into a pissing contest.

[@1973jdmc]

You are LOVED- thank you soooo sooooo very much.

[@OtiumAbscondita]

okay? So, basically

[@teresaibrahimi3903]

Complimenti abbastanza chiaro . Anche per me che non frequento nessun corso e studio in autodidattico per passione algebra astratta .

[@boblabaugh5097]

please become a math prof if you're not already

[@satyendrakumar-yz4ih]

Sir which books followed