Deck 19: Symmetry and Patterns

Question 1

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.

Answer 1

2, 1, 3, 4, 7, 11, 18

Question 2

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

Answer 2

for example,

Question 3

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?

Answer 3

The numbers drift toward the golden mean.

Question 4

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

Question 5

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

Question 6

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

Question 7

If the arithmetic mean and geometric mean of 7 and QUOTE are the same, what is the value of QUOTE ?

Question 8

Draw a wallpaper pattern that has only translation symmetries.

Question 9

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?

Question 10

Draw a strip pattern that has all possible symmetries.

Question 11

Draw a wallpaper pattern that has translation, rotation, and reflection symmetries.

Question 12

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.

Question 13

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

Question 14

Draw a strip pattern that has only translation and glide reflection symmetries.

Question 15

Find the difference between the golden mean $\phi$ and its reciprocal.

Question 16

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

Question 17

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

Question 18

Draw a figure that has both reflectional and rotational symmetry.

Question 19

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?

Question 20

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

Question 21

For Questions 35-37, use the following table for the Klein 4-group:
What is

Question 22

What are some of the isometries of a cube?

Question 23

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

Question 24

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

Question 25

For Questions 35-37, use the following table for the Klein 4-group:
What is the inverse of ?

Question 26

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

Question 27

What is the name of a pattern that exhibits similarity at ever finer scales?

Question 28

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

Question 29

For Questions 35-37, use the following table for the Klein 4-group:
What is

Question 30

How do pattern classification schemes aid anthropologists?

Question 31

How does the Sierpinski triangle illustrate an iterated function system?

Question 32

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

Question 33

Why do imperfect patterns sometimes pose a challenge to the classification scheme?

Question 34

Draw a shape that has exactly five lines of reflection symmetry.

Question 35

How many different wallpaper patterns are possible?

Question 36

Identify the elements of the symmetry group of a nonequilateral isosceles triangle.

Question 37

Draw a shape that has both reflection symmetry and rotational symmetry.

Question 38

How does a fern leaf demonstrate a fractal structure?

Question 39

What are the isometries of a circle?

Question 40

Identify the elements of the symmetry group of a square.

Question 41

What is the geometric mean of 9 and 81?

A) 27
B) 36
C) 45
D) another answer

Question 42

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

Question 43

What is the value of the product of the golden ratio $\phi$ and (1 − $\phi$ )?

A) 1
B) −1
C) $\phi$
D) another answer

Question 44

What is the name of the spiral pattern of shoots, leaves, or seeds around the stem of a plant?

Question 45

A rectangle has the dimension . If a square has the same area to the rectangle, what is the side length of the square?

A) arithmetic mean of and
B) geometric mean of and
C)
D) sum of and
Product of and

Question 46

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

A) S only
B) A only
C) E only
D) A and E only

Question 47

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

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

Question 48

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

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

Question 49

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 응 응 응 응 응 응 응 응

A) reflection
B) rotation
C) translation
D) All of the above.

Question 50

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

A) 42
B) 47
C) 55
D) 68

Question 51

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?

A) 18
B) 17
C) 15
D) 14

Question 52

What is the geometric mean of 4 and 16?

A) 8
B) 10
C) 12
D) another answer

Question 53

What is the geometric mean of the golden ratio and ?

A) 1
B)
C)
D)

Question 54

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

A) S only
B) A only
C) E only
D) A and E only

Question 55

The numbers 8 and 13 are consecutive Fibonacci numbers. What is the next Fibonacci number in the sequence?

A) 16
B) 18
C) 21
D) 26

Question 56

The value of the golden ratio is:

A) less than 1.
B) between 1 and 1.5.
C) between 1.5 and 2.
D) greater than 2.

Question 57

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

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

Question 58

What motions preserve the following strip pattern? Assume the pattern continues in both directions. 문 곰 문 곰 문 곰 문 곰

A) translation
B) glide reflection
C) reflection
D) both A and B

Question 59

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

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

Question 60

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?

A) 47
B) 41
C) 40
D) 32

Question 61

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

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

Question 62

Consider the following statement: "If three points are collinear, their images after an isometry are also collinear." This statement is:

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

Question 63

How many symmetry lines can a square have?

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

Question 64

How many symmetry lines can a regular pentagon have?

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

Question 65

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

A) translation and rotation only
B) translation and horizontal reflection only
C) translation, rotation, and vertical reflection only
D) translation, rotation, glide reflection, and vertical reflection

Question 66

Consider the following statement: "If four points form the corners of a square, their images after an isometry will also form a square." This statement is:

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

Question 67

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

A) translation and rotation only
B) translation and horizontal reflection only
C) translation and glide reflection only
D) translation, horizontal reflection, and vertical reflection

Question 68

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

A) translation only
B) translation and glide reflection only
C) translation and rotation only
D) translation, glide reflection, and rotation

Question 69

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

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

Question 70

How many different wallpaper patterns exist?

A) 7
B) 14
C) 17
D) 24

Question 71

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

A) translation only
B) translation and horizontal reflection only
C) translation and glide reflection only
D) translation, glide reflection, and vertical reflection

Question 72

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

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

Question 73

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

A) 3
B) 4
C) 6
D) 7

Question 74

How many different strip patterns exist?

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

Question 75

How many symmetry lines can a nonsquare rectangle have?

A) None
B) infinitely many
C) 2
D) 4

Question 76

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

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

Question 77

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

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

Question 78

How many elements are in the symmetry group of a square?

A) 2
B) 3
C) 4
D) 8

Question 79

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

A) translation and rotation only
B) translation and vertical reflection only
C) translation, rotation, and vertical reflection only
D) translation, rotation, glide reflection, and vertical reflection

Question 80

Consider the following statement: "If three numbered points are placed in a circle so that they increase from smallest to largest in clockwise order, their images after an isometry will also lie on a circle and increase from smallest to largest in clockwise order." This statement is:

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