“Projects” - Mathematics in Our World.

Following completion of your readings, complete exercise 4 in the “Projects” section on page 620 of Mathematics in Our World.

BELOW IS EXERCISE 4

Exercise 4 states that " the numbers 3, 4, and 5 are called Pythagorean triples cents 32 + 42 = 52. The number 5, 12, and 13 are also Pythagorean triples since 52 + 122 = 132. Can you find any of the Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples. Research the topic of Pythagorean triples and right a brief report on the subject."

1. Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.

2. After building your triples, verify each of them in the Pythagorean Theorem equation.

The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.

• Your introduction should include three to five sentences of general information about the topic at hand.

• The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.

• Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.  

Instructions

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  1.  Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.

2.   After building your triples, verify each of them in the Pythagorean Theorem equation.

The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.

    Your introduction should include three to five sentences of general information about the topic at hand.

    The body must contain a restatement of the problems and all math work, including the steps and formulas used to solve the problems.

    Your conclusion must comprise a summary of the problems and the reason you selected a particular method to solve them. It would also be appropriate to include a statement as to what you learned and how you will apply the knowledge gained in this exercise to real-world situations.

The assignment must be formatted according the APA (6th edition) style, which includes a title page and reference page. 

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MY EXAMPLES OF PYTHAGOREANS....I do not feel like writing a paper 

You can generate Pythagorean triples using the following expressions:

Pick two positive integers, m and n, with m less than n.

Then the three numbers that form the Pythagorean triple can be calculated from:

n² - m²

2mn

n² + m²

Examples:

1) m = 3, n = 4

n² - m² = (4)² - (3)² = 16 - 9 = 7

2mn = 2(3)(4) = 24

n² + m² = (4)² + (3)² = 16 + 9 = 25

Triple: 7, 24, 25

Check:

(7)² + (24)² = (25)²

49 + 576 = 625

625 = 625

2) m = 1, n = 3

n² - m² = (3)² - (1)² = 9 - 1 = 8

2mn = 2(1)(3) = 6

n² + m² = (3)² + (1)² = 9 + 1 = 10

Triple: 6, 8, 10

Check:

(6)² + (8)² = (10)²

36 + 64 = 100

100 = 100

3) m = 4, n = 5

n² - m² = (5)² - (4)² = 25 - 16 = 9

2mn = 2(4)(5) = 40

n² + m² = (5)² + (4)² = 25 + 16 = 41

Triple: 9, 40, 41

Check:

(9)² + (40)² = (41)²

81 + 1600 = 1681

1681 = 1681

4) m = 5, n = 6

n² - m² = (6)² - (5)² = 36 - 25 = 11

2mn = 2(5)(6) = 60

n² + m² = (6)² + (5)² = 36 + 25 = 61

Triple: 11, 60, 61

Check:

(11)² + (60)² = (61)²

121 + 3600 = 3721

3721 = 3721

5) m = 2, n = 4

n² - m² = (4)² - (2)² = 16 - 4 = 12

2mn = 2(2)(4) = 16

n² + m² = (4)² + (2)² = 16 + 4 = 20

Triple: 12, 16, 20

Check:

(12)² + (16)² = (20)²

144 + 256 = 400