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Creating Dihedral Group using Rotations and Reflections

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Tags: group-theorydihedral-groupabstract-algebramodern-algebranon-abelian-groupsymmetries-of-regular-polygon

In this video, we learn to create the Dihedral Group using Symmetric operations on basic shapes. For n>2, the nth Dihedral Group Dn is the group of symmetries of n sided regular polygon. This concept is depicted visually in the video which helps the viewer practically understand the concept of Dihedral Group and appreciate the beauty of mathematics. The video starts with introduction of symmetric operation on an equilateral triangle. Then, we first talk about properties of a group in simple terms for those who don't have a mathematics background. (Skip-able if you have studied about groups) Then we create the simplest Dihedral Group D1 using a straight line and D2 using a double sided arc polygon. We then proceed create D3 using an Equilateral triangle. We also show visually that D3 is Not Abelian. Then we create the elements of D4 using a square and write the generalized form of Dn, the nth Dihedral Group. The video ends with the presentation of the 12 elements of D6 using a regular Hexagon and 16 elements of D8 using a regular Octagon. Hope this video helps make this concept more fun and understandable.

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5.01 Overall score*

119 Rank

9 Votes

5 Comments

Comments

5.2

The animations are very well done, but the content feels bland and repetitive

Motivation is not really clear, why do this? The video is a bit monotonous.

6.4

Very well animated Competent execution To get a higher rating I would have liked to have seen some more depth, like a Cayley table and the graph structures of the group.

Nice presentation but isn’t really adding anything, this is straight from any introductory textbook on the subject.

Your English is really hard to understand. I appreciate the visuals but it is also possible to visualize the group itself. Many years ago, I was lucky to discover the book “Visual Group Theory” which builds a very good understanding of groups using Cayley graphs. It gives much better insight and appreciation of groups when seeing them as highly symmetrical structures. Adding Cayley diagrams for dihedral groups would make them more understandable.