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  2. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    There are many ways to prove Heron's formula, for example using trigonometry as below, or the incenter and one excircle of the triangle, [7] or as a special case of De Gua's theorem (for the particular case of acute triangles), [8] or as a special case of Brahmagupta's formula (for the case of a degenerate cyclic quadrilateral).

  3. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras .

  4. 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.

  5. Right triangle - Wikipedia

    en.wikipedia.org/wiki/Right_triangle

    The three sides of a right triangle are related by the Pythagorean theorem, which in modern algebraic notation can be written a 2 + b 2 = c 2 , {\displaystyle a^{2}+b^{2}=c^{2},} where c {\displaystyle c} is the length of the hypotenuse (side opposite the right angle), and a {\displaystyle a} and b {\displaystyle b} are the lengths of the legs ...

  6. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    The theorem states: T = I + 1 2 B − 1 {\displaystyle T=I+{\tfrac {1}{2}}B-1} where I {\displaystyle I} is the number of internal lattice points and B is the number of lattice points lying on the border of the polygon.

  7. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). [1] For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not.

  8. Special right triangle - Wikipedia

    en.wikipedia.org/wiki/Special_right_triangle

    Triangles based on Pythagorean triples are Heronian, meaning they have integer area as well as integer sides. The possible use of the 3 : 4 : 5 triangle in Ancient Egypt, with the supposed use of a knotted rope to lay out such a triangle, and the question whether Pythagoras' theorem was known at that time, have been much debated. [3]

  9. Kepler triangle - Wikipedia

    en.wikipedia.org/wiki/Kepler_triangle

    The Kepler triangle is named after the German mathematician and astronomer Johannes Kepler (1571–1630), who wrote about this shape in a 1597 letter. [1] Two concepts that can be used to analyze this triangle, the Pythagorean theorem and the golden ratio, were both of interest to Kepler, as he wrote elsewhere: