To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 1 2 distance apart.

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Answer 1

Question

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

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Answer 2

Question

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

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Answer 3

Question

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

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Answer 4

Question

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

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Answer 5

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

Answer 6

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

Answer 7

Chapter 3, Problem 19E

(a)

To determine

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

Answer 8

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

Answer 9

(b)

To determine

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

Answer 10

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

Answer 11

(c)

To determine

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 3 - Prob. 1E Ch. 3 - Prob. 2E Ch. 3 - Prob. 3E Ch. 3 - Prob. 4E Ch. 3 - Prob. 5E Ch. 3 - Prob. 6E Ch. 3 - Prob. 7E Ch. 3 - Use the pigeonhole principle to prove that the...Ch. 3 - Prob. 9E Ch. 3 - A child watches TV at least one hour each day for...

To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 1 2 distance apart.

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To prove: Any five points chosen within an equilateral triangle of side length 1, there are two of these five points which is at most 12 distance apart.

To prove: Any ten points chosen within an equilateral triangle of side length 1, there are two of these ten points which is at most 13 distance apart.

To prove: For an integer mn is such that if mn points are chosen within an equilateral triangle of side length 1, there are two of these mn points which is at most 1n distance apart.

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Chapter 3 Solutions