Pythagorean theorem information

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

\beta .\end{aligned}}} The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if γ {\displaystyle \gamma...

geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let A...

(the same for the three elements). The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the...

under-performing. The name comes from the formula's resemblance to the Pythagorean theorem. The basic formula is: W i n   R a t i o = runs scored 2 runs scored...

as its diameter. This is Thales' theorem. The legs and hypotenuse of a right triangle satisfy the Pythagorean theorem: the sum of the areas of the squares...

many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions...

statements of the Pythagorean theorem, both in the case of an isosceles right triangle and in the general case, as well as lists of Pythagorean triples. In...

The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric...

Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient...

are less than two right angles." (Book I proposition 17) and the Pythagorean theorem "In right-angled triangles the square on the side subtending the...

equilateral triangle as a {\displaystyle a} , we can determine using the Pythagorean theorem that: The area is A = 3 4 a 2 , {\displaystyle A={\frac {\sqrt {3}}{4}}a^{2}...

BC). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread...

catheti (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to...

setting of the geometric mean theorem there are three right triangles △ABC, △ADC and △DBC in which the Pythagorean theorem yields: h 2 = a 2 − q 2 h 2 =...

in ancient times for his supposed mathematical achievement of the Pythagorean theorem. Pythagoras had been credited with discovering that in a right-angled...

an approximation of the square root of 2 and the statement of the Pythagorean theorem. Baudhayana's Śrauta sūtras related to performing Vedic sacrifices...

the third square. This process can be continued indefinitely. The Pythagorean theorem that a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} can be proven...

corollaries to Thales's theorem. Pythagoras established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem, though the statement...

statement of the theorem proved is Theorem — The set {1, . . . , 7824} can be partitioned into two parts, such that no part contains a Pythagorean triple, while...

There is also the mathematical proof given in the treatise for the Pythagorean theorem. The influence of The Nine Chapters greatly assisted the development...

problems on the Papyrus may suggest that the ancient Egyptians knew the Pythagorean theorem. The Berlin Papyrus 6619 is an ancient Egyptian papyrus document...