Exam 19: Symmetry and Patterns

How many elements are in the symmetry group of the letter $R$ ?

What is the name of a pattern whose only symmetries are rotations about a single point and reflections through that point?

How many elements are in the symmetry group of an equilateral triangle?

Suppose a sequence begins 2, 1 and continues by adding the previous two numbers to determine the next number. What do the quotients of consecutive numbers drift toward?

Assume the following pattern continues in both directions. What isometries preserve the pattern?

How many elements are in the symmetry group of the regular pentagon shown below?

Draw a figure that has reflectional symmetry but no rotational symmetry.

Assume the following pattern continues in both directions. What isometries preserve the pattern?

Suppose a sequence begins with 1, 3 and continues by adding the previous two numbers to get the next number in the sequence. In this sequence, 7 and 11 are consecutive numbers. What is the next number in this sequence?

Which of these letters, S A E, has a shape that is preserved by a rotation isometry?

The symmetry group of a pattern always has: I: the identity element II: an even number of elements

Starting with 1,1, determine the next five Fibonacci numbers.

For the shape below, determine how many lines of symmetry exist.

Which of these letters, S A E, has a shape that is preserved by a reflection isometry?

Draw a wallpaper pattern that has only translation symmetries.

Suppose a sequence begins 1, 4 and continues by taking the geometric mean of the previous two numbers to determine the next number. What is the fourth term of the sequence?

Draw a shape that has reflection symmetry but no rotational symmetry.

For the shape below, determine how many lines of symmetry exist.

What are the isometries of a circle?

Assume the following pattern continues in both directions. What isometries preserve the pattern?