   Chapter 8.3, Problem 26ES Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

Solutions

Chapter
Section Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

We can form another symmetry group by using rotations of a square rather than of a triangle. Start with a square with corners labeled 1 through 4, placed in a reference square. The current position of the inner square is labeled I . We can rotate the inner square clockwise 90 ° to give an element of the group, R 90 . Similarly, we can rotate the square 180 ° or 270 ° to obtain the elements R 180 and R 270 . In addition, we can rotate the square about any of the lines of symmetry shown below. As before, the operation is “followed by," denoted by Δ . Refer to this symmetry group of the square.Find R r Δ R 180 .

To determine

Refer to symmetry group of square and find RrΔR180

Explanation

Calculation:

Considering the symmetry group of square, we need to find RrΔR180

Let the original square I as follows

Let us rotate the square about the vertical axis and then rotate through 90

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