Exam 19: Symmetry and Patterns

Suppose a sequence begins 1, 4 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?

Assume the pattern continues in all directions. What are the isometries of the pattern?

Assume the following patterns continue in both directions. Which of these patterns has a translation isometry? AAAAAAAAA ZZZZZZZZZ

What are some of the isometries of a cube?

Assume the pattern continues in all directions. What are the isometries of the pattern?

Draw a wallpaper pattern that has only translation and rotation symmetries.

Assume the following patterns continue in both directions. Which of these patterns has a rotation isometry?

Draw a strip pattern that has all possible symmetries.

Draw a figure that has both reflectional and rotational symmetry.

The numbers 21 and 34 are consecutive Fibonacci numbers. What is the next Fibonacci number in the sequence?

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

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, 18 and 29 are consecutive numbers. What is the next number in this sequence?

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

Suppose a wallpaper whose smallest rotation is 90° has reflection lines that intersect at 90° angles. Use the flowchart in the textbook to find the standard notation for the pattern.

Suppose a sequence begins 1, 4 and continues by adding the previous two numbers to determine the next number. Determine the next five numbers in this sequence.

Suppose a sequence begins with 1, 7 and continues by adding the previous two numbers to get the next number in the sequence. What number comes after 38 in this sequence?

How many symmetry lines can a nonsquare rectangle have?

Draw a wallpaper pattern that has only translation and reflection symmetries.

If the arithmetic mean and geometric mean of 7 and $\mathrm { x }$ are the same, what is the value of $\mathrm { x}$ ?