Question

6.2 perspective and symmetry 341
quick quiz 6.2
choose the best answer to each of the following questions. explain your reasoning with one or more complete sentences.
qq1. in a painting of train tracks that run perpendicular to the canvas, the principal vanishing point is
a. the place in the real scene where the train tracks disappear from view.
b. the place in the painting where the two rails meet.
c. the place in the painting where the rails first appear to touch the sky.
qq2. all lines that are parallel in a real - scene converge in a painting
a. at the principal vanishing point.
b. somewhere along the horizon line.
c. somewhere along the top edge of the painting.
qq3. study the last supper in figure 6.2.3. which of the following converge at the principal vanishing point?
a. parallel beams in the ceiling
b. lines connecting the heads of the disciples
c. the vertical sides of the doors and windows
qq4. the symmetry in da vincis sketch of the human body in figure 6.2.7 arises because
a. he shows two sets of arms and legs.
b. he has enclosed the bodies in a circle.
c. the left and right sides of the sketch are nearly mirror images of each other.
qq5. the letter w has reflection symmetry along a line
a. going diagonally through its middle.
b. going horizontally through its middle.
c. going vertically through its middle.
qq6. the letter z has
a. reflection symmetry.
b. rotation symmetry.
c. translation symmetry.
qq7. a perfect circle has
a. both reflection and rotation symmetry.
b. reflection symmetry only.
c. rotation symmetry only.
qq8. which of the following regular polygons cannot be used to make a tiling?
a. equilateral triangles
b. regular hexagons
c. regular octagons
qq9. suppose you arrange regular pentagons so that they are as close together as possible on a flat floor. the pattern will not be a tiling because
a. it will have gaps between some of the pentagons.
b. regular pentagons lack any type of symmetry.
c. tilings are possible only with three - and four - sided polygons.
qq10. a periodic tiling is one in which
a. only regular polygons are used.
b. only triangles are used.
c. the same pattern repeats over and over.
exercises 6.2
reading questions

1. describe the ideas of perspective and symmetry.
2. how is the principal vanishing point in a picture determined?
3. what is the horizon line? how is it important in a painting showing perspective?
4. briefly describe and distinguish among reflection symmetry, rotation symmetry, and translation symmetry. draw a simple picture that shows each type of symmetry.
5. what is a tiling? draw a simple example.
6. briefly explain why there are only three possible tiling patterns that consist of a single regular polygon. what are the three patterns?
7. briefly explain why more tilings are possible if we remove the restriction of using only regular polygons.
8. what is the difference between periodic and aperiodic tilings?

does it make sense?
decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). explain your reasoning.

1. the principal vanishing point of the painting is so far away that it cannot be seen in the painting.
2. sid does not need to use perspective in her ground - level painting of a flat desert because the desert is two - dimensional.

Explanation:

• QQ1: In perspective drawing, parallel lines that run perpendicular to the canvas converge at the principal vanishing point in the painting where the two rails meet.
• QQ2: Parallel lines in a real - scene converge at the principal vanishing point in a painting.
• QQ3: In "The Last Supper", parallel beams in the ceiling converge at the principal vanishing point.
• QQ4: The symmetry in da Vinci's sketch of the human body arises because the left and right sides of the sketch are nearly mirror images of each other.
• QQ5: The letter W has reflection symmetry along a line going vertically through its middle.
• QQ6: The letter Z has rotation symmetry.
• QQ7: A perfect circle has both reflection and rotation symmetry.
• QQ8: Regular pentagons cannot be used to make a tiling.
• QQ9: Regular pentagons will not form a tiling because there will be gaps between some of the pentagons.
• QQ10: A periodic tiling is one in which the same pattern repeats over and over.

Answer:

QQ1. b. the place in the painting where the two rails meet.
QQ2. a. at the principal vanishing point.
QQ3. a. parallel beams in the ceiling.
QQ4. c. the left and right sides of the sketch are nearly mirror images of each other.
QQ5. c. going vertically through its middle.
QQ6. b. rotation symmetry.
QQ7. a. both reflection and rotation symmetry.
QQ8. c. regular pentagons
QQ9. a. it will have gaps between some of the pentagons.
QQ10. c. the same pattern repeats over and over.