Math 123H - Symmetry
Questions on Readings

Questions on Hargittai & Hargittai

Q1: What is the difference between geometric symmetry and symmetry in nature or the real world?

Q2: How does the material we have already studied relate to the point group and space group symmetries (p. xvi, xvii) and to symmetry operations and symmetry elements (p. 2, 39)?  More specifically:
Q3: Why do they refer to a mirror plane rather than a mirror line?  Hint: where do the objects that Hargittai and Hargittai consider naturally live?  Where do the objects that we have reflected so far live?

Q4: Why do they refer to a rotation axis rather than a rotocenter on page 39?  Same type of hint as for Q3.

Q5: Explain the reason behind the "Fact to Consider" on page 68.  Do you agree with their statement that the "only case where reflection is not accompanied by rotation is when there is bilateral symmetry?

Q6: Is the comment on page 45 about jellyfish consistent with the discussion of symmetry in animals in Bunch, Chapter 1?  Explain.

Questions on Rosen

Q1 (Foreword, Preface, and Chapter 1):  How many symmetries does he view a square as having?  What are the additional symmetries and why do they arise?  (Describe the additional symmetries very precisely by specifying the necessary objects.  To explain why they arise it will be helpful to read the foreword.)

Q2 (Chapter 1):  Rosen takes a much broader view of what constitutes a symmetry transformation than we have so far.  Name 3 types of symmetry transformations that he mentions but we have not considered.

Q3 (Chapter 2):  Suppose the depressions labelled A, B, and C are arranged in an equilateral triangle with A at the top vertex, B at the bottom left vertex and C at the bottom right vertex.  Give the symmetries described on page 10 in terms of Farmer's standard notation (using r and m).  (It may help to draw out the triangle diagrams and show the effect of the maps Rosen describes on the diagram.  Remember that standard notation means the m is written on the left, but as always, the motion on the right is applied first.)

Q4 (Chapter 2):  Write an equation, using the symbols a and b to stand for two general symmetry transformations, that shows the property Rosen describes in the last three paragraphs of Chapter 2 (page 16-17) before the group theory section.  (Let a stand for covering the pot and b stand for filling the pot.  Notice that Rosen is discussing how to find the inverse of a combined transformation.  Write an equation for this using the symbols a and b.  It may help to think of this as translating the sentences on the bottom of page 16 and top of page 17 into symbols, or as translating part of Figure 2.13 into symbols.)

Q5:  Write one or more questions you have after reading Chapters 1 and 2.