WHat is the Pythagorean trio theory?

Answer 1

Ok. Everybody else is wrong, and needs to realize that everything you learn in skewl be WAK! Anyways, the pythagorean trio states that if a^2+b^2 =c^2, then a+b/2=c

Answer 2

As others already stated, a Pyth. trio is a set of natural numbers a <= b < c with the property that a^2 + b^2 = c^2.

A trio is called primitive if the three numbers have no common factors.

All primitive triples can be made as follows: choose two natural numbers x > y which have no factors in common. Calculate

a = 2 x y
b = x^2 - y^2
c = x^2 + y^2

For instance, if x = 5 and y = 2 we find the triple (a,b,c) = (20,21,29). Indeed,
20^2 + 21^2 = 400 + 441 = 841 = 29^2.

Proof that this is Pythagorean trio:
a^2 + b^2 =
... = (2 x y)^2 + (x^2 - y^2)^2
... = 4 x^2 y^2 + x^4 + y^2 - 2 x^2 y^2
... = x^4 + y^2 + 2 x^2 y^2
... = (x^2 + y^2)^2 = c^2

I am not going to prove here that all primitive trios can be made this way.

Answer 3

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.

The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational.

Answer 4

Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism.

Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term neopythagoreanism.
Pythagorean natural philosophy

Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras. On the other hand it is impossible to determine the origin of the Pythagorean account of substance. It seems that the Pythagorean account begins with Anaximander's account of the ultimate substance of things as "the boundless," by Anaximander called the "apeiron." On the other hand, the Pythagorean account says that it is through the notion of the "limit" that the "boundless" takes form.

Answer 5

A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.

Answer 6

The theory is named after the Greek mathematician Pythagoras.

The theory goes as follow:
In a right-angle triangle, the area of the square whose side is the hypotenuse (the side of a right-angle triangle opposite the right angle) is equal the sum of the areas of the two squares on the legs (A and B).

If (C) is the length of the hypotenuse and (A) and (B) be the
lengths of the other two sides, the theorem can be explained as

a^2 + b^2 = c^2


This theorem gives a simple relation between the three sides of a right-angle triangle so that if the lengths of any two sides are known, the length of the third side can be found.


This should clarify things.....

Answer 7

The Pythagorean Theorem
The Pythagorean Theorem computes the hypotenuse of a right triangle using the following relationship between the legs and the hypotenuse of a triangle:

The hypotenuse [c] equals the square root of the sum of the squares of each leg of the triangle [a and b].

Answer 8

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Answer 9

a^2 + b^2 = c^2
this is only valid for right angle triangles. That means one of the angle has to ne 90degrees.
And c is the opposite side to the right angle

Answer 10

If by trio you mean trig, that would be:

a[squared] + b[squared] = c[squared]

I hope.