The Pythagorean Theorem or Pythagoras' Theorem is a formula relating the lengths of the three sides of a right triangle. If we take the length of the hypotenuse to be c and the length of the legs to be a and b then this theorem tells us that:
The Pythagorean Theorem describes the lengths of the sides of a right triangle in a way that is so elegant and practical that the theorem is still widely used today. The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse.
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Pythagorean Theorem. Let's build up squares on the sides of a right triangle. Pythagoras' Theorem then claims that the sum of (the areas of) two small squares equals (the area of) the large one. In algebraic terms, a 2 + b 2 = c 2 where c is the hypotenuse while a and b are the sides of the triangle.
The Pythagorean Theorem can be interpreted in relation to squares drawn to coincide with each of the sides of a right triangle, as shown at the right. The theorem can be rephrased as, "The (area of the) square described upon the hypotenuse of a right triangle is equl to the sum of the (areas of the) squares described upon the other two sides."
Pythagorean Theorem Algebra Proof What is the Pythagorean Theorem? You can learn all about the Pythagorean Theorem, but here is a quick summary:. The Pythagorean Theorem says that, in a right triangle, the square of a (which is a×a, and is written a 2) plus the square of b (b 2) is equal to the square of c (c 2): a 2 + b 2 = c 2. Proof of the Pythagorean Theorem using Algebra
Given its long history, there are numerous proofs (more than 350) of the Pythagorean theorem, perhaps more than any other theorem of mathematics. The proofs below are by no means exhaustive, and have been grouped primarily by the approaches used in the proofs.
Beyond the Pythagorean Theorem. In the 17th century, Pierre de Fermat(1601-1665) investigated the following problem: For which values of n are there integral solutions to the equation x^n + y^n = z^n. We know that the Pythagorean theorem is a case of this equation when n = 2, and that integral solutions exist.
The Pythagorean Theorem is a statement in geometry that shows the relationship between the lengths of the sides of a right triangle – a triangle with one 90-degree angle. The right triangle equation is a 2 + b 2 = c 2. Being able to find the length of a side, given the lengths of the two other sides makes the Pythagorean Theorem a useful technique for construction and navigation.
Pythagoras, by tradition, is credited as the one who discovered the Pythagorean Theorem. However, it is known that the principles of the said theorem dates far back into earlier times. With what we know of Pythagoras and the antiquity of the said theorem we can only assume his authorship according to tradition.
The Pythagorean Theorem is believed to have been was discovered on a Babylonian tablet circa 1900-1600 B.C. The Pythagorean Theorem relates to the three sides of a right triangle.It states that c2=a2+b2, C is the side that is opposite the right angle which is referred to as the hypotenuse.