Deck 11: Mathematics and the Arts

Question 1

Provide an appropriate response.
The golden ratio was used in

A)the discovery of gold.
B)the value of
C)Greek architecture.
D)the building of the atomic bomb.

Answer 1

C

Question 2

Provide an appropriate response.
Which subject was not a part of the quadrivium - the standard curriculum in medieval universities?

A)geometry
B)history
C)astronomy
D)music

Answer 2

B

Question 3

Provide an appropriate response.
The golden ratio is an example of the use of

A)perspective.
B)proportion.
C)symmetry.
D)multiplication.

Answer 3

B

Question 4

Provide an appropriate response.
What fraction is approximately equal to the golden ratio?

A)
B)
C)
D)

Question 5

Provide an appropriate response.
What types of instruments create music digitally?

A)synthesizers
B)trombones
C)guitars
D)pianos

Question 6

Provide an appropriate response.
The vanishing point of a picture with perspective is

A)the point where you cannot see anything on the picture.
B)the point where parallel lines meet.
C)the point where two perpendicular lines intersect.
D)the point where two curves intersect.

Question 7

Provide an appropriate response.
Which of the following is an example of exponential growth?

A)the better the quality of sound
B)the increase in frequencies in scale
C)the change in height of a newborn baby
D)the number of notes in a song

Question 8

Provide an appropriate response.
The golden ratio divides a line into how many pieces?

A)two
B)one
C)four
D)three

Question 9

Provide an appropriate response.
Which of the following is not a type of symmetry?

A)translation
B)rotation
C)repetition
D)All of these.

Question 10

Provide an appropriate response.
One of the most basic qualities of sound is

A)string.
B)octave.
C)pitch.
D)analog.

Question 11

Provide an appropriate response.
Which music principle did the Greeks discover?

A)the shorter the string, the higher the pitch
B)the longer the string, the higher the pitch
C)the longer the string, the shorter the pitch
D)the shorter the string, the lower the pitch

Question 12

Provide an appropriate response.
When an object can be shifted, say to the left or right, and still remains the same, this is an example of symmetry.

A)rotation
B)translation
C)reflection
D)relation

Question 13

Provide an appropriate response.
The number of different tilings with irregular polygons is

A)limited; you can only make 3 different tilings using irregular polygons.
B)unlimited; you can make many different tilings using irregular polygons.
C)zero; you cannot make a tiling using irregular polygons.
D)limited; you can only make 1 different tiling using irregular polygons.

Question 14

Provide an appropriate response.
Which of the following is a method for storing digital music?

A)sheet music
B)floppy disk
C)compact disk
D)vinyl records

Question 15

Provide an appropriate response.
Which letter is an example of rotation symmetry?

A)C
B)S
C)T
D)R

Question 16

Provide an appropriate response.
Which regular polygon can be used to make a tiling?

A)pentagon
B)octagon
C)parallelogram
D)triangle

Question 17

Provide an appropriate response.
When making a tiling using only regular hexagons

A)the tiles fill all of the space, but there is some overlap of the tiles.
B)the tiles do not fill all of the space, there is some overlap of the tiles.
C)the tiles fill all of the space, with no overlaps and no gaps.
D)the tiles do not fill all of the space, there are gaps between the hexagons.

Question 18

Provide an appropriate response.
Which symbol do we use to denote the golden ratio?

A)
B)
C)
D)

Question 19

Provide an appropriate response.
On a painting using perspective there is a row of 6-story buildings extending from the foreground, all the way to the vanishing point. The buildings in the background

A)appear to be the same size as the ones in the foreground.
B)appear smaller than the ones in the foreground.
C)appear larger than the ones in the foreground.
D)None of these.

Question 20

Provide an appropriate response.
In mathematics, the word symmetry is used

A)to describe an operation that changes appearance.
B)to describe an operation that leaves something unchanged.
C)to draw an obtuse angle.
D)when a solution to an equation is unknown.

Question 21

Provide an appropriate response.
What is the first principle of perspective?

A)All parallel lines never intersect, they remain the same distance apart.
B)All shapes and sizes must remain equal, regardless of their distance from the viewer.
C)All lines that are parallel in the real scene and perpendicular to the canvas must intersect at the principal vanishing point of the painting.
D)None of these.

Question 22

Find the frequencies of the first 6 notes of the scale that starts at the given note.
C# above middle C; this C# has a frequency of 275

Question 23

Provide an appropriate response.
What is one way to decide if two numbers follow a Fibonacci sequence?

A)if their ratio is approximately the same as the golden ratio
B)if each number is a multiple of the next
C)if each number is prime
D)if their sum is the same as their difference

Question 24

Provide an appropriate response.
Which regular polygon can be used to make a tiling with a single polygon?

A)octagon
B)dodecahedron
C)heptagon
D)hexagon

Question 25

Provide an appropriate response.
The golden ratio is a(n)

A)whole number.
B)natural number
C)rational number.
D)irrational number.

Question 26

Provide an appropriate response.
Draw an object with rotation symmetry.

Question 27

Find the frequencies of the first 6 notes of the scale that starts at the given note.
A# above middle C; this A# has a frequency of 463

Question 28

Provide an appropriate response.
What are the most pleasing combinations of notes?

A)first harmonics
B)consonant tones
C)fourths
D)fifths

Question 29

Provide an appropriate response.
Draw an object with reflection symmetry.

Question 30

Form a tiling from the given figure using translations and reflections.

Question 31

Write the word or phrase that best completes each statement or answers the question.
Draw an object with translation symmetry.

Question 32

Form a tiling from the given figure using translations and reflections.

Question 33

Provide an appropriate response.
Which of these is not a type of picture of music?

A)digital
B)color
C)analog
D)All of the above

Question 34

Provide an appropriate response.
In how many ways does the golden ratio occur in a pentagram?

A)at least ten
B)none
C)five
D)eight

Question 35

Form a tiling from the given figure using translations and reflections.

Question 36

Form a tiling from the given figure using translations and reflections.

Question 37

Provide an appropriate response.
Which letter is an example of reflective symmetry?

A)G
B)R
C)K
D)Q

Question 38

Form a tiling from the given figure using translations and reflections.

Question 39

Provide an appropriate response.
Which item is not related to the golden ratio?

A)the golden pitch
B)Fibonacci sequences
C)logarithmic spiral
D)the golden rectangle

Question 40

Provide an appropriate response.
What question led Greek scholars to formulating the golden ratio?

A)How are pitch and vibration related?
B)How to find π?
C)What is the square root of 2?
D)What is the best way to divide a line?

Question 41

Provide an appropriate response.
Given 2.2 inches is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation

A)3.56 in. or 0.74 in.
B)5.76 in. or 1.19 in.
C)5.76 in. or 0.84 in.
D)3.56 in. or 1.36 in.

Question 42

Identify all of the symmetries in the following figure.

Question 43

Solve.
Given 0.22 centimeters is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation

A)0.36 cm or 0.14 cm
B)0.58 cm or 0.08 cm
C)0.36 cm or 7.36 cm
D)0.58 cm or 11.91 cm

Question 44

Provide an appropriate response.
Starting with a tone having a frequency of 579 cycles per second, find the frequency of the tone that is two octaves higher.

A)2316 cps
B)1158 cps
C)4632 cps
D)335,241 cps

Question 45

Provide an appropriate response.
The circle of fifths is generated by starting at a particular musical note and stepping upward by intervals of a fifth. By what factor does the frequency of a tone increase if it is raised by three fifths?

A)22.35
B)1.22
C)6.05
D)3.36

Question 46

Provide an appropriate response.
Starting at middle D with a frequency of 292 cps, find the frequency of the note a fifth above middle D.

A)274
B)432
C)437
D)459

Question 47

Provide an appropriate response.
Starting with a tone having a frequency of 159 cycles per second, find the frequency of the tone that is four octaves higher.

A)636 cps
B)1272 cps
C)2544 cps
D)25,281 cps

Question 48

Provide an appropriate response.
Starting at middle D with a frequency of 292 cps, find the frequency of the note a an octave and a fourth above middle D.

A)801
B)779
C)761
D)774

Question 49

Provide an appropriate response.
Given 1.6 inches is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation

A)2.59 in. or 1.01 in.
B)2.59 in. or 0.99 in.
C)4.19 in. or 1.64 in.
D)4.19 in. or 0.61 in.

Question 50

Provide an appropriate response.
Starting at middle G with a frequency of 390 cps, find the frequency of the note 36 half-steps above middle G.

A)3156
B)3084
C)3115
D)3120

Question 51

Provide an appropriate response.
Starting at middle D with a frequency of 292 cps, find the frequency of the note five half-steps above middle D.

A)412
B)385
C)390
D)274

Question 52

Provide an appropriate response.
Draw two cubes, one with perspective and one without.

Question 53

Solve.
Given 5.1 kilometers is one side of a golden rectangle, find the length of the other side. Notice that the other side could be either longer or shorter than the given side. Use the approximation

A)8.26 km or 0.32 km
B)13.36 km or 0.51 km
C)13.36 km or 1.95 km
D)8.26 km or 3.15 km

Question 54

Provide an appropriate response.
Starting with a tone having a frequency of 122 cycles per second, find the frequency of the tone that is three octaves higher.

A)488 cps
B)366 cps
C)976 cps
D)14,884 cps

Question 55

Identify all of the symmetries in the following figure.

A)It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the
Same. It also has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its
Appearance remains the same.
B)It has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same.
C)It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the
Same.
D)None of these.

Question 56

Identify all of the symmetries in the following figure.

A)It has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its appearance remains the same. It also has translation symmetry.
B)It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the
Same. It also has rotation symmetries; it can be rotated through 90°, 180°, or 270°, and its
Appearance remains the same.
C)It has reflection symmetries; it can be reflected across a vertical line through its center or a horizontal line through its center, and its appearance remains the same. It also has rotation
Symmetry; it can be rotated through 180° and its appearance remains the same.
D)None of these.

Question 57

Solve.
A line is subdivided according to the golden ratio, with the smaller piece having a length of 7 meters. What is the length of the entire line?

A)36.4 m
B)14 m
C)18.2 m
D)11.2 m

Question 58

Provide an appropriate response.
Starting with middle F, at a frequency of 347 cycles per second, find the frequency of the next octave of F in the circle of fifths.

A)431
B)29,148
C)44,416
D)22,208

Question 59

Provide an appropriate response.
Starting with a tone having a frequency of 154 cycles per second, find the frequency of the tone that is one octave higher.

A)616 cps
B)308 cps
C)23,716 cps
D)462 cps

Question 60

Provide an appropriate response.
Starting with a tone having a frequency of 761 cycles per second, find the frequency of the tone that is three octaves higher.

A)3044 cps
B)579,121 cps
C)6088 cps
D)2283 cps

Question 61

Provide an appropriate response.
Starting with a tone having a frequency of 105 cycles per second, find the frequency of the tone that is two octaves higher.

A)315 cps
B)11,025 cps
C)840 cps
D)420 cps

Question 62

Identify all of the symmetries in the following figure.

A)It has translation symmetry (if imagined to extend in both directions). It also has reflection symmetry (across a horizontal line between the jagged lines).
B)It has rotation symmetry; it can be rotated through 180° and its appearance remains the same. It also has translation symmetry (if imagined to extend in both directions).
C)It has reflection symmetries; it can be reflected across a vertical line through its center, a horizontal line through its center, or either of its diagonals, and its appearance remains the
Same.
D)None of these.