Pythagorean Triples
Ashley Walker
MAT126
Bridget Simmons
November 28, 2011

A Pythagorean triple 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 Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer) (Vargas, 2008). In project #4, pg. 522, (Mathematics in Our World) introduced some new information to add to my mathematics knowledge of numbers. The numbers 3, 4, and 5 are called Pythagorean triples since 32 + 42 = 52. The numbers 5, 12, and 13 are also Pythagorean triples since 52 + 122 = 132. Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples and write a brief report on the subject (Bluman, 2005). When asked to find any other Pythagorean triples, I found 5, choosing 2 integers, m and n, with m less than n (Manuel, 2010). Three formulas I choose to form the Pythagorean triple, which can be calculated from: n2 – m2

...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...

...PythagoreanTriples
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...

...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...

...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...

...ancient Greek mathematician and philosopher. Pythagoras was responsible for important developments in the history of mathematics, astronomy, and the theory of music.
The thing that Pythagoras is probably the most famous for is the Pythagorean Theorem. The Pythagorean Theorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides. This means that if...

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