Assignment 9

Week 9 Reading

Read the rest of Brown. Pay particular attention to the problem 15 in section 1.8 (page 36), all of section 1.9 and sections 2.5, 2.6, and 2.7. In HSGAS, read section 6.3.

Assignment 9 (45+ points, Due Monday, 11/27)
9.1 Point Symmetry (5 points)

State which triangles have point symmetry and prove your statement.

State which quadrilaterals have point symmetry and prove your statement.

9.2 Two circles (5 points)

HSGAS, 6.3.1, #1

9.3 Intersection of a figure with a line of symmetry (5 points)

HSGAS, 6.3.1, #5

9.4 Symmetries of graphs (5 points)

HSGAS 6.3.2 #10

9.5 Symmetries of square graph paper (5 points)

Imagine the pattern of a sheet of graph paper of squares, extended to infinity by translating the pattern horizontally and vertically. You will be given a sheet of such paper. On the sheet, indicate all the symmetries of this pattern on the plane – the lines of symmetry, the centers of rotational symmetry, the vectors of translation symmetry (since the number is infinite, you can stop when you have made the pattern clear). Colored pen or pencil may help make this clear.

9.6 Symmetries of parallelogram graph paper (5 points)

Imagine the pattern of a sheet of graph paper of parallelograms, extended to infinity by translating the pattern in the directions of the sides of the parallelograms. You will be given a sheet of such paper. On the sheet, indicate all the symmetries of this pattern on the plane as explained in 9.5.

9.7 Symmetries of parallelogram graph paper (5 points)

Imagine the pattern of a sheet of graph paper of rhombi, extended to infinity by translating the pattern in the directions of the sides of the rhombi. This is a tessellation of the plane. You will be given a sheet of such paper. On the sheet, indicate all the symmetries of this pattern on the plane as explained in 9.5.

9.8 Symmetries of gift wrap paper, etc. (10 points or more)

Find an example of a symmetric pattern covering the whole plane from real life (gift wrap paper, wall paper, book or magazine illustration). This will be a finite part of a pattern that can be extended to fill the plane by translations. Choose an example that has more than translation symmetries (and the pattern should already show the translations--no fair showing the letter S and saying "translate it"). Make a copy of this pattern and turn it in(photocopy, computer printout, photograph, etc.)

Write up a complete analysis of the symmetries of the pattern and on a separate sheet draw an accurate "skeleton" figure with just the centers of rotational symmetry, the lines of reflection or glide reflection, and the translations.