# Lecture 2 - 2 Examples of Symmetry groups Suppose that we...

This preview shows pages 1–2. Sign up to view the full content.

2. Examples of Symmetry groups Suppose that we take an equilateral triangle and look at its symmetry group. There are two obvious sets of symmetries. First one can rotate the triangle through 120 . Suppose that we choose clockwise as the posi- tive direction and denote rotation through 120 as R . It is natural to represent rotation through 240 as R 2 , where we think of R 2 as the effect of applying R twice. If we apply R three times, represented by R 3 , we would be back where we started. In other words we ought to include the trivial symmetry I , as a symmetry of the triangle (in just the same way that we think of zero as being a number). Note that the symmetry rotation through 120 anticlockwise, could be represented as R - 1 . Of course this is the same as rotation through 240 clockwise, so that R - 1 = R 2 . The other obvious sets of symmetries are flips. For example one can draw a vertical line through the top corner and flip about this line.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern