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History of pythagoras' theorem pdf

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Pythagorean theorem

Relation between sides of a right triangle

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.

The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation:^[1]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proved numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squ

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Pythagorean Theorem

The Pythagorean theorem is a fundamental result in Euclidean geometry that relates the side lengths of a right triangle through the simple relationship a² + b² = c². The relationship was known to the ancient scholars and builders of Babylon, Egypt, China and India. While Pythagoras lived and wrote from 569–475 BCE, the result that now bears his name appeared as early as 1800 BCE in surviving clay Babylonian tablets. The Pythagorean theorem was also known to early Chinese scholars and appeared in the sacred texts of ancient India related to altar building.

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Satz des Pythagoras

Dieser Eintrag war in der 52. Woche
des Jahres 2016 das Wort der Woche.

Satz des Pythagoras (Deutsch)

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Wortverbindung, Substantiv, m

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Worttrennung:

Satz des Py·tha·go·ras, kein Plural

Aussprache:

IPA:[ˈzat͡s dɛs pyˈtaːɡoʁas]

Hörbeispiele:Satz des Pythagoras^(Info)

Bedeutungen:

[1] Mathematik:fundamentaler Satz der euklidischenGeometrie, welcher besagt, dass in allen ebenen rechtwinkligenDreiecken die Summe der Flächeninhalte der Kathetenquadrate gleich dem Flächeninhalt des Hypotenusenquadrates ist

Symbole:

[1] a² + b² = c²

Herkunft:

benannt nach Pythagoras von Samos, der als Erster dafür einen mathematischen Beweis gefunden haben soll, was allerdings in der Forschung umstritten ist^[1]

Synonyme:

[1] Hypotenusensatz, Lehrsatz von Pythagoras, Pythagoräischer Lehrsatz, Satz von Pythagoras

Oberbegriffe:

[1] Lehrsatz, Theorem

Beispiele:

[1] „Anders formuliert besagt der Satz des Pythagoras, dass die Summe der Flächeninhalte der beiden Quadrate über den Katheten gle