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  2. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    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.

  3. Pythagorean field - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_field

    A superpythagorean field F is a formally real field with the property that if S is a subgroup of index 2 in F ∗ and does not contain −1, then S defines an ordering on F. An equivalent definition is that F is a formally real field in which the set of squares forms a fan. A superpythagorean field is necessarily Pythagorean. [12]

  4. Bride's Chair - Wikipedia

    en.wikipedia.org/wiki/Bride's_Chair

    The name Bride's Chair is also used to refer to a certain diagram attributed to the twelfth century Indian mathematician Bhaskara II (c. 1114–1185) who used it as an illustration for the proof of the Pythagorean theorem. [7] The description of this diagram appears in verse 129 of Bijaganita of Bhaskara II. [8]

  5. Power of a point - Wikipedia

    en.wikipedia.org/wiki/Power_of_a_point

    Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .

  6. Tree of primitive Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Tree_of_primitive...

    [6]: p.7 For example, parent (3, 4, 5) has excircle radii equal to 2, 3 and 6. These are precisely the inradii of the three children (5, 12, 13), (15, 8, 17) and (21, 20, 29) respectively. If either of A or C is applied repeatedly from any Pythagorean triple used as an initial condition, then the dynamics of any of a , b , and c can be ...

  7. Pythagoras number - Wikipedia

    en.wikipedia.org/wiki/Pythagoras_number

    In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p ( K ) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.

  8. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).

  9. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.