a) To find: Whether the work used in the painting is one point perspective, two point, or both.

Question

| Without evaluating the Legendre symbols, prove the following. (i) 1(173)+2(2|73)+3(3|73) +...+72(72|73) = 0. (Hint: As r runs through the numbers 1,2,. (ii) 1²(1|71)+2²(2|71) +3²(3|71) +...+70² (70|71) = 71{1(1|71) + 2(2|71) ++70(70|71)}. 72, so does 73 – r.)

Answer 1

Question

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

To determine

b)

To describe:

The location of vanishing point.

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

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| Without evaluating the Legendre symbols, prove the following. (i) 1(173)+2(2|73)+3(3|73) +...+72(72|73) = 0. (Hint: As r runs through the numbers 1,2,. (ii) 1²(1|71)+2²(2|71) +3²(3|71) +...+70² (70|71) = 71{1(1|71) + 2(2|71) ++70(70|71)}. 72, so does 73 – r.)

By considering the number N = 16p²/p... p² - 2, where P1, P2, … … … ‚ Pn are primes, prove that there are infinitely many primes of the form 8k - 1.

(c) (i) By first considering the case where n is a prime power, prove that n μ² (d) = ø(n) (d)' n≥ 1. d\n (ii) Verify the result of part (c)(i) when n = 20.

Answer 2

Question

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

To determine

b)

To describe:

The location of vanishing point.

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

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Answer 3

Question

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

To determine

b)

To describe:

The location of vanishing point.

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Expert Solution & Answer

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Answer 4

Question

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

To determine

b)

To describe:

The location of vanishing point.

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

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Answer 5

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

To determine

b)

To describe:

The location of vanishing point.

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Answer 6

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

Answer 7

Chapter 8.6, Problem 15E

To determine

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

Answer 8

To determine

b)

To describe:

The location of vanishing point.

Answer 9

To determine

b)

To describe:

The location of vanishing point.

Answer 10

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

Answer 11

To determine

c)

To describe:

The location of vanishing point for small features given in painting such as table.

Answer 12

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

Answer 13

To determine

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

Answer 14

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

Answer 15

To determine

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

Answer 16

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

Answer 17

To determine

f)

To find:

Whether the painting has pavement or not if so describe where.

Answer 18

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

Answer 19

To determine

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

Answer 20

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Answer 21

To determine

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Answer 22

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Answer 33

Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - Prob. 4E Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - In Exercise 9 and 10, find a the area and b the...Ch. 8.1 - Prob. 10E

a) To find: Whether the work used in the painting is one point perspective, two point, or both.

Solution Summary: The author explains that the painting uses one-point perspective, in which there is only one vanishing point, and the wall faces are parallel to the surface.

Videos

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

b)

To describe:

The location of vanishing point.

c)

To describe:

The location of vanishing point for small features given in painting such as table.

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

f)

To find:

Whether the painting has pavement or not if so describe where.

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Chapter 8 Solutions

a) To find: Whether the work used in the painting is one point perspective, two point, or both.

Solution Summary: The author explains that the painting uses one-point perspective, in which there is only one vanishing point, and the wall faces are parallel to the surface.

Videos

a) To find: Whether the work used in the painting is one point perspective, two point, or both.

b) To describe: The location of vanishing point.

c) To describe: The location of vanishing point for small features given in painting such as table.

d) To describe: Whether the painting has two separate vanishing points. If so, describe the location.

e) To find: Whether the painting use foreshortening or not if so, describe location.

f) To find: Whether the painting has pavement or not if so describe where.

g) To find: Whether the painting has Albertian grid on the ceiling or walls.

h) To find: Whether the painting’s horizons line an actual part of the painting or not if so then find the location.

Chapter 8 Solutions

a)

To find:

Whether the work used in the painting is one point perspective, two point, or both.

b)

To describe:

The location of vanishing point.

c)

To describe:

The location of vanishing point for small features given in painting such as table.

d)

To describe:

Whether the painting has two separate vanishing points. If so, describe the location.

e)

To find:

Whether the painting use foreshortening or not if so, describe location.

f)

To find:

Whether the painting has pavement or not if so describe where.

g)

To find:

Whether the painting has Albertian grid on the ceiling or walls.

h)

To find:

Whether the painting’s horizons line an actual part of the painting or not if so then find the location.