Pythagorean Triples
To begin you must understand the Pythagoras theorem is an equation of a2 + b2 = c2. This simply means that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest. Let a, b, and c be the three sides of a right angled triangle. To define, a right angled triangle is a triangle in which any one of the angles is equal to 90 degrees. The longest side of the right angled triangle is called the 'hypotenuse'. Once you have this basic understanding you can apply the understanding that if a, b, and c are positive integers, they are called Pythagorean Triples. Our textbook explains that “the numbers 3, 4, and 5 are called Pythagorean triples since 32 + 42 = 52” (Bluman, pg. 522) and that there is a set of formulas that will generate an infinite number of Pythagorean triples. Here are some examples:

| | |
3,4,5 Triangle 5,12,13 Triangle 9,40,41 Triangle| | | 32 + 42 = 52 52 + 122 = 132 92 + 402 = 412(Ganesh, 2010.)| | | The set of Pythagorean Triples is endless. Let n be any integer greater than 1 as in this example which is a set of Pythagorean triple, is true because: (3n)2 + (4n)2 = (5n)2 Some other Pythagorean Triples are (5,12,13); (7,24,25); (8,15,17); (9,40,41); (17,144,145); and (25,312,313).| | | To summarize, it is fairly easy to show that no matter what numbers you use for n you can use this method to show that there are infinitely many Pythagorean Triples. Since the Pythagorean Theorem states that every right triangle has side lengths satisfying the formula a2 + b2 = c2; the Pythagorean triples describe the three integer side lengths of a right triangle.

References:
Bluman, A. G. (2005). Mathematics in Our World (1st Ed.) Ashford University, Custom Edition. New York: McGraw-Hill. Ganesh, J. (2010). Pythagorean Triples...

...PythagoreanTriples
Ashley Walker
MAT126
Bridget Simmons
November 28, 2011
A Pythagoreantriple is a triple of positive integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (Bluman, 2005). A Pythagoreantriple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are...

...Pythagorean Theorem
Diana Lorance
MAT126
Dan Urbanski
March 3, 2013
Pythagorean Theorem
In this paper we are going to look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagoreantriples and asks if you can find more Pythagoreantriples than the two that are listed which are (3,4, and 5) and (5,12, and 13) (Bluman, 2012). The...

...five more PythagoreanTriples 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.
Exercise #4:
The numbers 3, 4, and 5 are called Pythagoreantriples since 32+42=52. The numbers 5, 12, and 13 are also Pythagoreantriples since 52+122=132. Can you find any other...

...Anmol Mehrotra
Pythagoreantriples
Math Bonus
A
Pythagoreantriple
consists of three positive
integers
a
,
b
, and
c
, such
2
2
2
that
a
+
b
=
c
. Such a triple is commonly written (
a
,
b
,
c
), and a
wellknown example is (3, 4, 5). If (
a
,
b
,
c
) is a Pythagoreantriple, then so
is (
ka
,
kb
, ...

...The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
The Pythagorean Theorem is Pythagoras' most...

...Farhrenheit = 1.8 x (Celsius) + 32
8. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. For example, if two sides of a right triangle have lengths 3 and 4, then the hypotenuse must have a length of 5. The integers 3, 4, and 5 together form a Pythagoreantriple. There is an infinite number of such triples. Given two positive integers, m and n,...

...Assignment: Pythagorean Quadratic
Algebra has been around for many years. Some people feel there is no use for algebra in the real world. There are those who feel it is a waste of time because only certain professions really use it. However, algebra is used in many ways which can relate to everyday situations. Algebra truly is a part of our everyday life and there really is no escaping it. This week, we are asked to solve a problem using the Pythagorean...

...PYTHAGOREAN THEOREM
More than 4000 years ago, the Babyloneans and the Chinese already knew that a triangle with the sides of 3, 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three, the second side four and the last side five sections long, they could easily construct a right angle.
A Greek scholar named Pythagoras, who lived around 500...

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