You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
What is the pathagorian therom?
- Thread starter NATALI
- Start date
Re: pathagorian therom
The Pythagoreans are thought to have been the first to truly appreciate the concept of numbers. One of the areas of their concentration was square numbers, such as 4, 9, 16, 25, 36, and so on. They reportedly discovered that the sums of certain pairs of square numbers, or perfect squares, were also square numbers.
History records that Pythagoras and Diophantus were probably the two most well known mathematicians that had anything to do with right triangles with integer sides. The famous Pythagorean Theorem states that in any right-angled triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Another way of stating it is that the area of the square constructed on the long side of a right triangle is equal to the area of the two squares created on the two shorter sides. This is expressed by x^2 + y^2 = z^2.
Almost everyone has heard of the famous 3-4-5 right triangle where 3^2 + 4^2 = 5^2, the simplest, and most fundamental triangle based on the Pythagorean theorem. Surprisingly, fewer people know of the 5, 12, and 13 right triangle, or the 7, 24, and 25 right triangle, which also satisfy the relationship and without any proportional relationship to the 3, 4, and 5 triangle. These sets of three integers, all satisfying the Pythagorean theorem, are traditionally referred to as Pythagorean Triples, of which there are an infinite number.
When all three sides of a Pythagorean triangle are integers, they are referred to as a Pythagorean Triple. Pythagorean Triples that have a greatest common divisor of 1 are called primitive triples. Those with factors other than 1 are called non-primitive triples.
Primitive Pythagorean Triples of the form x^2 + y^2 = z^2 can be derived from x = m^2 - n^2, y = 2mn, and z = m^2 + n^2 where "m" and 'n" are arbitrary positive integers of opposite parity (one odd one even), and "m" is greater than "n". (For x, y, & z to be a primitive solution, "m" and "n" must have no common factors and must not both be even or odd. Dropping these two limitations will produce non-primitive Pythagorean Triples.
NATALI said:What is the pathegorian therum?
The Pythagoreans are thought to have been the first to truly appreciate the concept of numbers. One of the areas of their concentration was square numbers, such as 4, 9, 16, 25, 36, and so on. They reportedly discovered that the sums of certain pairs of square numbers, or perfect squares, were also square numbers.
History records that Pythagoras and Diophantus were probably the two most well known mathematicians that had anything to do with right triangles with integer sides. The famous Pythagorean Theorem states that in any right-angled triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Another way of stating it is that the area of the square constructed on the long side of a right triangle is equal to the area of the two squares created on the two shorter sides. This is expressed by x^2 + y^2 = z^2.
Almost everyone has heard of the famous 3-4-5 right triangle where 3^2 + 4^2 = 5^2, the simplest, and most fundamental triangle based on the Pythagorean theorem. Surprisingly, fewer people know of the 5, 12, and 13 right triangle, or the 7, 24, and 25 right triangle, which also satisfy the relationship and without any proportional relationship to the 3, 4, and 5 triangle. These sets of three integers, all satisfying the Pythagorean theorem, are traditionally referred to as Pythagorean Triples, of which there are an infinite number.
When all three sides of a Pythagorean triangle are integers, they are referred to as a Pythagorean Triple. Pythagorean Triples that have a greatest common divisor of 1 are called primitive triples. Those with factors other than 1 are called non-primitive triples.
Primitive Pythagorean Triples of the form x^2 + y^2 = z^2 can be derived from x = m^2 - n^2, y = 2mn, and z = m^2 + n^2 where "m" and 'n" are arbitrary positive integers of opposite parity (one odd one even), and "m" is greater than "n". (For x, y, & z to be a primitive solution, "m" and "n" must have no common factors and must not both be even or odd. Dropping these two limitations will produce non-primitive Pythagorean Triples.
Re: pathagorian therom
Please spell this way: Pythagorean theorem
Now go study here: http://en.wikipedia.org/wiki/Pythagorean_theorem
NATALI said:What is the pathegorian therum?
Please spell this way: Pythagorean theorem
Now go study here: http://en.wikipedia.org/wiki/Pythagorean_theorem