FTS-100, Symmetry: Beauty, Order and
Homework for Chapter 4
Answer each of the following problems as clearly and concisely as you can.
Label each problem clearly, and show your work or explain your reasoning.
This homework is due on November 18
at the beginning of class.
Homework for Chapter 3
Do exercise 4.2.7 on page 42. Essentially you
need to draw border patterns using human feet. Be sure to draw one
pattern of each type. Next try to move your feet in that border pattern
and figure out which of the seven names fit your motion.
Explain why a border pattern that has both a horizontal
reflection symmetry and a half-turn symmetry must also have a vertical
Answer each of the following problems as clearly and concisely as you
can. Label each problem clearly, and show your work or explain your
reasoning. This homework is due on October
30 at the beginning of class.
Last modified: November 14, 2002
A regular polygon is a polygon where all the angles
have the same size and all the sides have the same length.
How many symmetries does a regular triangle have?
Describe them precisely and concisely (in words).
How many symmetries does a regular pentagon have?
Describe them precisely and concisely.
Suppose n is an odd number. Describe
the symmetries of a regular n-gon (a regular polygon with n
sides) precisely and concisely.
Using the multiplication table for the regular pentagon,
express each of the symmetries below as a single symmetry.
Assume that r is the first rotation and that m is the first
Sketch a finite figure whose symmetry type is C4.
Sketch another one whose symmetry type is D4. Both of your figures
must be different from the ones ins the text and the ones we used in class.
Find the multiplication table for the symmetries
of a regular hexagon.