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American Association for the Advancement of Science (1993). Benchmarks for science literacy. New York: Oxford University Press. ISBN 9780195089868. Bruton, Sheila; Ong, Faye (2000). Science content standards for California public schools : kindergarten through grade twelve (PDF). Sacramento, Calif.: Dept. of Education. ISBN 978-0-8011-1496-0
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between 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.
In 1988, The Theorem of Pythagoras was the first video produced by the series and reviews the Pythagorean theorem. [4] For all right triangles, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a 2 + b 2 = c 2). The theorem is named after Pythagoras of ancient Greece.
In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines. Prominent careers for professional mathematicians include math teacher or professor, statistician , actuary , financial analyst , economist , accountant , commodity trader , or computer consultant .
The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, [216] [214] [217] [218] but he may have been the first to introduce it to the Greeks. [ 219 ] [ 217 ] Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof . [ 220 ]
Carl Friedrich Gauss is credited with an 1820 proposal [1] for a method to signal extraterrestrial beings in the form of drawing an immense right triangle and three squares on the surface of the Earth, intended as a symbolical representation of the Pythagorean theorem, large enough to be seen from the Moon or Mars.
In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...
The book provided illustrated proof for the Pythagorean theorem, [31] contained a written dialogue between of the earlier Duke of Zhou and Shang Gao on the properties of the right angle triangle and the Pythagorean theorem, while also referring to the astronomical gnomon, the circle and square, as well as measurements of heights and distances. [32]