Skills Check

Skills Check

Question 19.1

1. Symmetry includes notions of

  1. balance.
  2. similarity.
  3. repetition.
  4. all of the above.

1.

d

Question 19.2

2. Many people think that mathematics is just about numbers, but in fact mathematics includes the study of _________________.

2.

patterns

Question 19.3

3. Which of the following rectangles is closest to the aspect ratio of a golden rectangle?

  1. 16 by 9
  2. 13 by 6
  3. 11 by 8

3.

a

Question 19.4

4. The geometric mean of 4 and 36 is _____________.

4.

12

Question 19.5

5. Which artist claimed to use the golden ratio in his work?

  1. Leonardo da Vinci
  2. Wolfgang Amadeus Mozart
  3. Neither

5.

c

Question 19.6

6. In the Fibonacci sequence, _________ is the next element after 21.

6.

34

Question 19.7

7. Recursion means

  1. cursing over and over.
  2. giving a next number in terms of previous ones.
  3. giving previous numbers in terms of the current one.

7.

b

Question 19.8

8. Of pineapples, pine beetles, and pine bark, only ___________ exhibit Fibonacci numbers.

8.

pineapples

Question 19.9

9. Phyllotaxis is

  1. the town in Pennsylvania where fractals were invented, near Fillodoughphia.
  2. more taxis than you need.
  3. a spiral pattern in plants.

9.

c

Question 19.10

10. The geometric mean of 4, 16, and 125 is ____________.

10.

20

Question 19.11

11. A rigid motion always moves any pair of points

  1. in the same direction.
  2. to another pair of points the same distance apart.
  3. to their mirror images.

11.

b

Question 19.12

12. The capital letters ______, ______, ______, ______, ______, ______, and ______ each have a rotation isometry.

12.

H; I; N; O; S; X; Z

Question 19.13

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

  1. only
  2. only
  3. Neither

13.

b

Question 19.14

14. This strip pattern

⌟⌜ ⌟⌜ ⌟⌜ ⌟⌜ has _________ and _________ isometries.

14.

translation; rotation

Question 19.15

15. What isometries does this wallpaper pattern have?

image
  1. Translation and reflection only
  2. Translation and rotation only
  3. Translation, rotation, and reflection

15.

c

Question 19.16

16. This wallpaper pattern

has ________ and ________ isometries.

image

16.

translation; reflection (along diagonal lines)

Question 19.17

17. If a horizontal strip pattern has a glide reflection isometry, then

  1. it always has a horizontal reflection isometry.
  2. it may also have a horizontal reflection isometry.
  3. it cannot have a horizontal reflection isometry.

814

17.

b

Question 19.18

18. If a strip pattern has both vertical and horizontal reflection isometries, then it always has a ___________ isometry.

18.

half-turn rotation

Question 19.19

19. Consider the strip pattern in the raffia cloth held by the woman in the photo at right. What isometries does it have?

image
  1. Vertical reflection
  2. Horizontal reflection
  3. Glide reflection

19.

c

Question 19.20

20. There are _____ ways to repeat a pattern along a strip.

20.

7

Question 19.21

21. The key mathematical idea for detecting and analyzing patterns is

  1. cataloging possible motifs.
  2. figuring out the symmetries.
  3. looking for the golden ratio.

21.

b

Question 19.22

22. The symbol indicates that a strip pattern has ____________ symmetry.

22.

translation

Question 19.23

23. The symbol 2 indicates that a pattern has

  1. rotational symmetry.
  2. reflection symmetry.
  3. too much symmetry.

23.

a

Question 19.24

24. The symbol indicates that a wallpaper pattern has _____________________ symmetry.

24.

reflection

Question 19.25

25. The symmetry group of a nonsquare rectangle has how many elements?

  1. 4
  2. 6
  3. 8

25.

a

Question 19.26

26. The symmetry group of the strip pattern has ___________ elements.

26.

infinitely many

Question 19.27

27. The symmetry group of a square has how many elements?

  1. 2
  2. 4
  3. 8

27.

c

Question 19.28

28. In the mattress group, the result of a flip followed by a rotation is a _______________.

28.

toss

Question 19.29

29. In mathematics, chaos refers to

  1. randomness.
  2. disorder.
  3. unpredictability.

29.

c

Question 19.30

30. A fractal is a pattern that exhibits ____________ at ever finer scales.

30.

self-similarity