Question 1

How many different strip patterns exist?

Accepted Answer

A)  4 
B)  7 
C)  17 
D)  24 
A)  4 
B)  7 
C)  17 
D)  24 B

Question 2

Find the difference between the golden mean F1F1F1S1F1F1F10 and its reciprocal.

Accepted Answer

1

Question 3

How do pattern classification schemes aid anthropologists?

Accepted Answer

They describe patterns in a formal scheme.

Question 4

Consider the following statement: "The image of a right-side print after an isometry is a left-side print." This statement is:

Accepted Answer

A)  always true. 
B)  sometimes true, depending on the isometry. 
C)  never true. 
A)  always true. 
B)  sometimes true, depending on the isometry. 
C)  never true.

Question 5

What is the value of the product of the golden ratio F1F1F1S1F1F1F10 and (1 − F1F1F1S1F1F1F10)?

Accepted Answer

A)  1 
B)  −1 
C)  F1F1F1S1F1F1F10 
D)  another answer 
A)  1 
B)  −1 
C)  F1F1F1S1F1F1F10 
D)  another answer

Question 6

If a figure has two reflection symmetries across perpendicular lines, it:

Accepted Answer

A)  always has a rotation symmetry. 
B)  sometimes has a rotation symmetry. 
C)  never has a rotation symmetry. 
A)  always has a rotation symmetry. 
B)  sometimes has a rotation symmetry. 
C)  never has a rotation symmetry.

Question 7

How many symmetry lines can a square have?

Accepted Answer

A)  2 
B)  4 
C)  8 
D)  infinitely many 
A)  2 
B)  4 
C)  8 
D)  infinitely many

Question 8

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

Accepted Answer

A)  I only 
B)  II only 
C)  both I and II 
D)  neither pattern 
A)  I only 
B)  II only 
C)  both I and II 
D)  neither pattern

Question 9

A group is commutative if $x \circ y = y \circ x$ for any two elements x and y in the group. Is the Klein 4-group commutative?

Accepted Answer

A) True 
 B)False

Question 10

Suppose a wallpaper pattern with only a 180° rotation has reflection lines that always intersect at a rotational center. Use the flowchart in the textbook to find the standard notation for the pattern.

Accepted Answer

A)  pmm 
B)  cmm 
C)  pmg 
D)  p2 
A)  pmm 
B)  cmm 
C)  pmg 
D)  p2

Question 11

Is it possible for a wallpaper pattern to have a translation and glide reflection isometries but no reflection isometry?

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A)  AAAAAAAAA only 
B)  ZZZZZZZZZZ only 
C)  both AAAAAAAAA and ZZZZZZZZZ 
D)  neither pattern 
A)  AAAAAAAAA only 
B)  ZZZZZZZZZZ only 
C)  both AAAAAAAAA and ZZZZZZZZZ 
D)  neither pattern

Question 13

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

Accepted Answer

A)  AAAAAAAAA only 
B)  ZZZZZZZZZZ only 
C)  both AAAAAAAAA and ZZZZZZZZZ 
D)  neither pattern 
A)  AAAAAAAAA only 
B)  ZZZZZZZZZZ only 
C)  both AAAAAAAAA and ZZZZZZZZZ 
D)  neither pattern

Question 14

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

Accepted Answer

A)  1 
B)  2 
C)  4 
D)  6 
A)  1 
B)  2 
C)  4 
D)  6

Question 15

Suppose a sequence begins 2, 1 and continues by adding the previous two numbers to determine the next number. Determine the next five numbers in this sequence.

Accepted Answer

2, 1, 3, 4

Question 16

How does the geometric mean of two numbers compare with their arithmetic mean?

Accepted Answer

The geometric mean i

Question 17

How many symmetry lines can a regular pentagon have?

Accepted Answer

A)  5 
B)  10 
C)  20 
D)  infinitely many 
A)  5 
B)  10 
C)  20 
D)  infinitely many

Question 18

What is the geometric mean of the golden ratio $\phi$ and ($\phi-1$) ?

Accepted Answer

A)  1 
B)  $\phi$ 
C)  $\phi-1$ 
D)  $\phi^{2}$ 
A)  1 
B)  $\phi$ 
C)  $\phi-1$ 
D)  $\phi^{2}$

Question 19

Identify the elements of the symmetry group of a square.

Accepted Answer

the identity, 1/4 turn, 1/2 tu

Question 20

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

Accepted Answer

A)  I only 
B)  II only 
C)  both I and II 
D)  neither pattern 
A)  I only 
B)  II only 
C)  both I and II 
D)  neither pattern

Exam 19: Symmetry and Patterns

How many different strip patterns exist?

Find the difference between the golden mean  and its reciprocal.

How do pattern classification schemes aid anthropologists?

Consider the following statement: "The image of a right-side print after an isometry is a left-side print." This statement is:

What is the value of the product of the golden ratio  and (1 − )?

If a figure has two reflection symmetries across perpendicular lines, it:

How many symmetry lines can a square have?

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

A group is commutative if x∘y=y∘xx \circ y = y \circ xx∘y=y∘x for any two elements x and y in the group. Is the Klein 4-group commutative?

Suppose a wallpaper pattern with only a 180° rotation has reflection lines that always intersect at a rotational center. Use the flowchart in the textbook to find the standard notation for the pattern.

Is it possible for a wallpaper pattern to have a translation and glide reflection isometries but no reflection isometry?

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

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

How many elements are in the symmetry group of the letter HHH ?

Suppose a sequence begins 2, 1 and continues by adding the previous two numbers to determine the next number. Determine the next five numbers in this sequence.

How does the geometric mean of two numbers compare with their arithmetic mean?

How many symmetry lines can a regular pentagon have?

What is the geometric mean of the golden ratio ϕ\phiϕ and ( ϕ−1\phi-1ϕ−1 ) ?

Identify the elements of the symmetry group of a square.

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

Urban Services

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Tilings

Savings Models

Borrowing Models

The Economics of Resources

Filters

A group is commutative if $x \circ y = y \circ x$ for any two elements x and y in the group. Is the Klein 4-group commutative?

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

What is the geometric mean of the golden ratio $\phi$ and ( $\phi-1$ ) ?