Week 5 Assignment you Mat 126

 Week 4 Assignment you Mat 126 Essay

Week 4 Assignment one particular

MAT 126

August 5th 2013

Pursuing completion of your readings, total exercise 5 in the " Projects” section on page 620 of Math concepts in Our Universe. In the two step process is to sure you build or perhaps generate in least five more Pythagorean Triples making use of the many formulations available online for doing this. Then after building the triples, verify each of them in the Pythagorean Theorem equation.

The Pythagorean Theorem will be based upon Euclidian Angles among the relationship between the 3 sides of your right triangular which essentially states a2+b2=c2. Or the reality a2 = one aspect of the correct triangle + b2 sama dengan 2nd area of the proper triangle means C2 or the hypotenuse.

Just for this assignment I actually figured I would personally do 2 proof types for each double. For any all-natural number m> 1,

a2+b2=c2

(2m)2 + (m2-1)2 sama dengan (m2+1)2

Example1:

m= 5

2m sama dengan 8 sama dengan side A of proper

m2-1 sama dengan 15 sama dengan side N of correct

m2+1 = 17 = side C of the right (Hypotenuse)

Pythagorean triple (8, 15, 17)

Proof:

(2m)2 + (m2-1)2 = (m2+1)2

(2*4)2+(42-1)2=(42+1)2

(8)2+(16-1)2=(16+1)2

64+225=289

Proof2:

a2+b2=c2

82+152=172

64+225=289

Example2:

m=6

2m=12 = part A of right

m2-1 = thirty-five = side B of right

m2+1 = thirty seven = side C of the right (Hypotenuse)

Pythagorean multiple (12, thirty five, 37)

Proof1:

(2m)2 + (m2-1)2 sama dengan (m2+1)2

(2*6)2+(62-1)2=(62+1)2

(12)2+(36-1)2=(36+1)2

144+1225=1369

Proof2:

a2+b2=c2

122+352=372

144+1225=1369

Example3:

m=7

2m=14 sama dengan side A of right

m2-1 = 48 sama dengan side M of right

m2+1 = 50 = side C of the right (Hypotenuse)

Pythagorean triple (14, 48, 50)

Proof1:

(2m)2 + (m2-1)2 = (m2+1)2

(2*7)2+(72-1)2=(72+1)2

(14)2+(49-1)2=(49+1)2

196+2304=2500

Proof2:

a2+b2=c2

142+482=502

196+2304=2500

Example4:

m=8

2m=16 = side A of right

m2-1 = 63 = part B of right

m2+1 = 65 = part C of the right (Hypotenuse)

Pythagorean double (16, 63, 65)

Proof1:

(2m)2 & (m2-1)2 sama dengan (m2+1)2...

Sources: Bluman, A. G. (2011). Mathematics inside our world (1st ed. Ashford University Custom). United States: McGraw-Hill.


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