## CHECK THESE SAMPLES OF Pythagorean triples

6 Pages(1500 words)Research Paper

...Ionian and **Pythagorean** views The first Greek philosophers who laid the foundation of the recorded and well-known philosophical works of Plato and Aristotle were the Ionians and the **Pythagorean**. They also influence the works of succeeding revolutionary scientists such as Galileo, Copernicus, Newton and even Einstein in the modern period. Their scientific philosophies also underpin the theoretical and basic methodological approaches of current scientific practice. It can be said that the Ionian School with its naturalist approach in observing the world and phenomena provided the empirical or inductive method that is seen as one way of arriving at scientific knowledge. The **Pythagoreans** on the other hand, with their basic conception... of...

4 Pages(1000 words)Case Study

...**Pythagorean** Triplets **Pythagorean** triplets are integer solutions to the **Pythagorean** Theorem. Pythagoras lived around 500 BC, but **Pythagorean** triplets were first recorded as far back as 1700-1800 BC in Babylonia, inscribed on a clay tablet, known as Plimpton 322. A large number of integer pairs (a,c) for which there is an integer b satisfying Pythagoras' equation were systematically listed on it.
Let a, b, and c be positive real numbers. Then c is the length of the hypotenuse of a right triangle with side lengths a, b, and c if and only if;
a2 + b2 = c2
The **Pythagorean** triplet is an ordered triplet (a, b, c) of three positive integers such that
a2 + b2...

2 Pages(500 words)Essay

...the alteration of the scale of logarithms from the hyperbolic 1 / e from which John Napier had given to that which unity is assumed as the logarithm of the ratio of 10 to 1 [2]. During their conversation, the alteration proposed by Briggs was agreed upon by Napier and published the first chiliad of his logarithms during his second visit to Edinburgh in 1617. In 1624 Henry Briggs gave a numerical approximation to the base 10 logarithm.
**Pythagorean** Brotherhood
The **Pythagorean** Brotherhood is one of Greece's ancient societies. **Pythagoreans**, as the members were called combined philosophy and politics. This so-called brotherhood was established by Pythagoras, a Greek philosopher...

5 Pages(1250 words)Essay

...THE **PYTHAGOREAN** THEOREM [Source: http www.arcytech.org/java/pythagoras/preface.html] April 30, 2008 The **Pythagorean** Theorem In mathematics, the **Pythagorean** Theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras who lived in the 6th century B.C.
The theorem is as follows:
"In any right angle triangle, the area of the square of the side opposite the right angle i.e. whose side is the hypotenuse is equal to the sum of the areas of the squares of the two sides that meet at a right angle i.e. whose sides are the two legs"
In other words
The square on the hypotenuse is equal to the sum of the squares on the other two sides
Geometric... ...

14 Pages(3500 words)Essay

...**Pythagorean** **Triples** A **Pythagorean** **triple** refers to the three positive integers, a,b, and c, in the **Pythagorean** equation a2 + b2 = c2. These three positive integers represent the three sides of a right triangle. Suppose we have m and n which are both positive integers at which mPythagorean **triple** which represents the values of a,b, and c.
In this assignment, we are required to generate five more **Pythagorean** **Triples**.
1. [8,6,10]
2. [12,16,20]
3. [9,40,41]
4. [91,60,109]
5. [28,96,100]
After identifying five **triples**, we should verify each of them using the **Pythagorean** Theorem equation.
1. [8,6,10] let a = 8, b = 6, and c = 10
a2 + b2 = c2
82 + 62 = 64 + 36 = 100
102 = 100
2. [12,16,20] let a = 12... , b = 16, and c = 20
a2 + b2 = c2
122 + 162 = 144 + 256 = 400
202 = 400
3. [9,40,41] let a = 9, b = 40, and c = 41
a2 + b2 = c2
92 + 402 = 81 + 1600 = 1681
412 = 1681
4. [91,60,109] let a = 91, b = 60, and c = 109
a2 + b2 = c2
912 + 602 = 8281 + 3600 = 11881
1092 = 11881
5. [28,96,100] let a = 28, b = 96, and c = 100
a2 + b2 = c2
282 + 962 = 784 + 9216 = 10000
1002 = 10000
In all the **triples** identified, it was verified that a, b, and c are in...

1 Pages(250 words)Essay

...**Pythagorean** Theorem (Add (Add (Add
**Pythagorean** Theorem
Introduction
Evidences show that **Pythagorean** Theorem was popular even among ancient civilizations. This famous theorem was developed by the Greek mathematician and philosopher Pythagoras. Historical writings argue that though Babylonian mathematicians had knowledge in the theorem, they could not develop it into a mathematical framework. Unlike any other mathematical theorem, the **Pythagorean** Theorem is supported by both geometric and algebraic...

3 Pages(750 words)Essay

...by the transcendence done by Lindemann which stated that the circle could not be squared. Lastly, the Twentieth Century idiosyncrasies exposed the division between analytical and computational studies. Ramanujans Modular Equations and Approximations exhibits a remarkable series for 1/ π.
4. The number 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 .More **Pythagorean** **triples** include; 8,15 and 17. 9,20 and 41(92+402=412). 12,13 and 37(122+132=37 2). 13,84 and 85(132+842=852). 15,112and 113( 152+ 1122+1132) . 16,63 and 65(162+632=652)....

2 Pages(500 words)Speech or Presentation

...**Pythagorean** **Triples** A **Pythagorean** **triple** refer to a set of three positive integers a, b, c such that the sum of the squares of two smaller integers of them equal to the square of the third largest integer i.e. if c > a, b then a2 + b2 = c2, c2 – a2= b2, or, c2 – b2 = a2. **Pythagorean** **triples** are part of **Pythagorean** Theorem which says that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides 1. Each **triple** set has its many multiples which will be regarded as the same **triple** set i.e. the set (a, b, c) and its any multiple k, ka, kb, kc,...

1 Pages(250 words)Speech or Presentation

...**Pythagorean** Theorem and Quadratic Equation Introduction Discovered and developed by scientist and mathematician, Pythagoras (c. 570 BC – c. 495 BC),‘**Pythagorean** Theorem’ is a widely applied mathematical statement which illustrates the relation of the three sides of a right triangle that consists of two legs and a longest side, known as the hypotenuse. In equation, it is given by --
c2 = a2 + b2
where the variables ‘a’ and ‘b’ refer to the length measures of the right triangle’s legs while the variable ‘c’ pertains to the hypotenuse. Applications of **Pythagorean** Theorem are recognized in various fields of maths such as algebra, trigonometry, and calculus.
Problem 98: ...

1 Pages(250 words)Speech or Presentation