Why nobody is talking about how cool it is that he snaps his fingers to clean the board? As mathematics teacher I create my own videos as well and this gives me great ideas! Love this video.
Your channel is so good. It's wonderful to watch this more advanced stuff; it takes me back to my undergraduate days and all those happy memories. Best wishes to you from the UK.
This absolutely is the same for me. These video's take me back to my first years studying math at my uni and also it brings the joy of understanding the material better than back in those early years.
The drawings starting around 7:50, combining rotation and reflexion of an n-gon presuppose that n is odd. Strictly speaking you should check that the result is the same when n is even.
At 10:00, it should be n-1 clockwise rotations (r^n-1) followed by a reflection that fixes 1 (s) to be consistent. What you did was n-1 counter-clockwise rotations (r^(n-1))^(n-1), following by a reflection that fixes n (which is not s).
We must be careful not to confuse rotation as being restricted to it's common definition of rotating through 2pi or 360 degrees. In this context a rotation means a "motion." If not then writing that the number of rotations=2(pi) K/n where k is )=k-< or equal to n-1 is confusing. Example: Set n=3 (a triangle) we have that 2(pi) k/3- the number of rotations, implying K=9/2(pi) which is about 3/2( not even an integer in the set[0,N-1} . It's about one and a half rotations which certainly note equal to what is correct:3 .
Why nobody is talking about how cool it is that he snaps his fingers to clean the board? As mathematics teacher I create my own videos as well and this gives me great ideas! Love this video.
Finally I got the concept totally! Thank you very much for this clear and wonderful explanation!
Your channel is so good. It's wonderful to watch this more advanced stuff; it takes me back to my undergraduate days and all those happy memories. Best wishes to you from the UK.
This absolutely is the same for me. These video's take me back to my first years studying math at my uni and also it brings the joy of understanding the material better than back in those early years.
OMG This is gold .
Love my math instructor but me not taking number theory has been a set back.
THANK YOU
This Is my Man right there! One of my favorite videos all Time.
The previous video is czcams.com/video/rapZj9yqsNw/video.html
thank you
Love your channel so much. Thanks for sharing.
another proof of rs=sr^(n-1):
note that they are inverses. Because they are both reflections,it must be the case that they are equal.
Nice and quick!
Brilliant!
The drawings starting around 7:50, combining rotation and reflexion of an n-gon presuppose that n is odd. Strictly speaking you should check that the result is the same when n is even.
nice,in the end the r^(k+1)=s*r^n*r^n-(k+1)
I love this explanation I can relate with it a lot thank you for loading on time
Thanks
At 10:00, it should be n-1 clockwise rotations (r^n-1) followed by a reflection that fixes 1 (s) to be consistent. What you did was n-1 counter-clockwise rotations (r^(n-1))^(n-1), following by a reflection that fixes n (which is not s).
Best explanation
We must be careful not to confuse rotation as being restricted to it's common definition of rotating through 2pi or 360 degrees. In this context a rotation means a "motion." If not then writing that the number of rotations=2(pi) K/n where k is )=k-< or equal to n-1 is confusing. Example: Set n=3 (a triangle) we have that 2(pi) k/3- the number of rotations, implying K=9/2(pi) which is about 3/2( not even an integer in the set[0,N-1} . It's about one and a half rotations which certainly note equal to what is correct:3 .
Great
Just a small nitpick, but I think you forgot to include closure in your definition of a group
* being a binary operation requires closure under * by definition
Plz define dicyclic group in soft manners
17:10 Check the last line of the proof, guys.
Yes, I caught that error.
Aren’t there 4 axioms of groups? You seem to miss closure.
A group is a set combined with a binary operation, meaning the operation is already closure
why Quentin Tarantino is making math videos?