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...

mathematical problem", in part because the theorem has the largest number of unsuccessful proofs. The Pythagorean equation, x2 + y2 = z2, has an infinite...

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...

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

Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem invented by James A. Garfield (November 19, 1831 – September 19...

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...

of squares of the amplitudes). Geometrically, it is a generalized Pythagorean theorem for inner-product spaces (which can have an uncountable infinity...

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...

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

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}...

} which has been described as "a sort of demented version of the Pythagorean theorem". If two circles are replaced by lines, the tangency between the...

{\displaystyle h_{c}={\sqrt {pq}}}   (Geometric mean theorem; see Special Cases, inverse Pythagorean theorem) For acute triangles, the feet of the altitudes...

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...

In geometry, a Bride's Chair is an illustration of the Pythagorean theorem. The figure appears in Proposition 47 of Book I of Euclid's Elements. It is...

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 =...

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...

a common point of intersection. The theorem can also be thought of as a generalization of the Pythagorean theorem. For a triangle △ A B C {\displaystyle...

orthogonal to v . {\displaystyle \mathbf {v} .} ) We can thus apply the Pythagorean theorem to u = ⟨ u , v ⟩ ⟨ v , v ⟩ v + z {\displaystyle \mathbf {u} ={\frac...

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

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...

In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron...

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