Pythagorean theorem
The Pythagorean theorem is a fundamental relation in Euclidean geometry. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. The theorem, whose history is the subject of much debate, is named for the ancient Greek thinker Pythagoras. It has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power.
About Pythagorean theorem in brief
The Pythagorean 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 is equal to the sum of the areas of the squares on the other two sides. The theorem, whose history is the subject of much debate, is named for the ancient Greek thinker Pythagoras. It 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 theorem may have more known proofs than any other ; the book The Pythagoreans contains 370 proofs. Recent scholarship has cast increasing doubt on any sort of role for Pythagora as a creator of mathematics, although debate about this continues. If the lengths of both a and b are known, then c can be calculated as. The law of cosines, which allows the computation of the length of any side of any triangle, reduces to the Pythagorian equation if the angle between the other sides is a right angle. The 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. The triangle postulate: CBH is also similar to triangle ABC, because they both have the same right angle and they share a similar reasoning, meaning that the third angle will be the same in both triangles.
By the same reasoning, CBH can be used to postulate ACH, which is similar to ABC. The result equates to the equality of ratios of the corresponding angles of the cosines of the angles, whereas the first equates their sines. The second equates the result of equating the sines of θ, which equates to H, which equates H and e, and the third equates CBH, C, D, E, H, and CBH. The postulate can be written asSumming these two equalities, after simplification, expresses the Pythagean theorem: Q. The role of this proof in the history of mathematics is much speculation in why this proof is why the postulate is so popular. This proof requires the similarity of the angle in two triangles is equivalent to the parallel angles in two parallel triangles, and is the equivalent to CBH being the same as ABC. It can be found in the book Euclid’s Elements, by D. D. Heath, and mentions the proposals of Bretschneider and Hankel that Pythagoris may have known this proof, and that he made it in the first five centuries after Euclid’s Elements. Theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclideans, and indeed, to objects that aren’t triangles at all, but n-dimensional solids.
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This page is based on the article Pythagorean theorem published in Wikipedia (as of Dec. 09, 2020) and was automatically summarized using artificial intelligence.
