Essay of pythagorean theorem
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The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to the legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that square root of 2 is irrational
and, therefore cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers.
The Pythagorean theorem states that: "The area of the square built on the hypotenuse of a right triangle is equal to the sum of the squares on the remaining two sides."
Around Two thousand five hundred years ago, a Greek mathematician, Pythagoras, invented the Pythagorean Theorem. The Theorem was related to the length of each side of a right-angled triangle. In a right-angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the sum of the squares on the other two sides. (148, Poskitt) To know more about this famous theorem, we can look at the other forms of the Pythagorean Theorem, such as it can also be written as c^2-a^2=b^2 which is for reverse operations like finding side b with the data of a and c. Meanwhile, the proofs of the theorem can make us understand more about the invention of the theorem and how Pythagoras figured it out.
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Step-by-step explanation:
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation"
where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. The theorem, whose history is the subject of much debate, is named for the ancient Greek thinker Pythagoras.
The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound.
This proof is based on the proportionality of the sides of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles.
There is debate whether the Pythagorean theorem was discovered once, or many times in many places, and the date of first discovery is uncertain, as is the date of the first proof. Historians of Mesopotamian mathematics have concluded that the Pythagorean rule was in widespread use during the Old Babylonian period (20th to 16th centuries BC), over a thousand years before Pythagoras was born. The history of the theorem can be divided into four parts: knowledge of Pythagorean triples, knowledge of the relationship among the sides of a right triangle, knowledge of the relationships among adjacent angles, and proofs of the theorem within some deductive system.
ritten between 2000 and 1786 BC, the Middle Kingdom Egyptian Berlin Papyrus 6619 includes a problem whose solution is the Pythagorean triple 6:8:10, but the problem does not mention a triangle. The Mesopotamian tablet Plimpton 322, written between 1790 and 1750 BC during the reign of Hammurabi the Great, contains many entries closely related to Pythagorean triples.
In India, the Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th and 5th century BC, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle. The Apastamba Sulba Sutra (c. 600 BC) contains a numerical proof of the general Pythagorean theorem, using an area computation. Van der Waerden believed that "it was certainly based on earlier traditions". Carl Boyer states that the Pythagorean theorem in Śulba-sũtram may have been influenced by ancient Mesopotamian math, but there is no conclusive evidence in favor or opposition of this possibility.