Art Theory

Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics



Professor Macauley

Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics

Groups are always lurking where symmetry arises. In this lecture, we explore many beautiful examples of groups that arise from natural symmetries in science, art, and mathematics. This includes shapes of molecules, repeating patterns in 1, 2, and 3 dimensions, and finally, how groups arise in braids.

Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html

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25 thoughts on “Visual Group Theory, Lecture 1.3: Groups in science, art, and mathematics
  1. I read a book about particle physics, "Deep Down Things" and they talk a little about Group Theory and then Lie Groups so I thought I would try to learn the basics of Group Theory since it sounds interesting.

  2. How math should've been created:
    Dude: bro, think sbout this.
    Bro: makes no sense, dude.
    Dude: bro, wants me to draw?
    Bro: I doubt u can, dude.
    Dude – invents math

  3. In the 2/7 Frieze, shouldn't there be also a "negative" glide reflection? Otherwise we would not be able to "undo" any action – i.e. we won't have a reverse for each action. Same question for T in the 1/7 and 6/7 Frieze.

  4. ~ 18:45 I don't understand why the 2nd one on the left requires a horizontal (over a vertical axis) reflection… wouldn't a translation+glide or even just 2x glide reflection be enough? Same for any, I don't see the need for the horizontal flip as a generator for any of them.

  5. does the Cayley diagram for the frieze work? in the frieze pattern gr^2 = f but this doesn't seem to be the case in the Cayley diagram??

  6. Hi,
    If only actions are allowed that preserve the footprint, the horizontal flip at 12:30 should not be a permitted acition. Also if it is indistinguishable, does that not represent the Identity action?

  7. On 12:30 Do you mean that doing a glide reflection after doing the gh (glide to the right and then horizontal flip), is a glide reflection that glides to the left?

  8. At 26:54 I think you missed -1 in the answer exponent. S1 S3^-1 S1^-1 = S3^-1
    Just saying, but I like your videos and I will keep watching them. Thank you 😉

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