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  2. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    The formula is credited to Heron (or Hero) of Alexandria (fl. 60 AD), [3] and a proof can be found in his book Metrica. Mathematical historian Thomas Heath suggested that Archimedes knew the formula over two centuries earlier, [ 4 ] and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible ...

  3. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    Heron of Alexandria found what is known as Heron's formula for the area of a triangle in terms of its sides, and a proof can be found in his book, Metrica, written around 60 CE.

  4. Methods of computing square roots - Wikipedia

    en.wikipedia.org/wiki/Methods_of_computing...

    A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...

  5. Hero of Alexandria - Wikipedia

    en.wikipedia.org/wiki/Hero_of_Alexandria

    Hero of Alexandria (/ ˈ h ɪər oʊ /; Ancient Greek: Ἥρων [a] ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also known as Heron of Alexandria / ˈ h ɛr ən /; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era.

  6. Brahmagupta's formula - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta's_formula

    Heron's formula for the area of a triangle is the special case obtained by taking d = 0. The relationship between the general and extended form of Brahmagupta's formula is similar to how the law of cosines extends the Pythagorean theorem .

  7. Cayley–Menger determinant - Wikipedia

    en.wikipedia.org/wiki/Cayley–Menger_determinant

    Menger extended Cayley's algebraic results to propose a new axiom of metric spaces using the concepts of distance geometry up to congruence equivalence, known as the Cayley–Menger determinant. This ended up generalising one of the first discoveries in distance geometry, Heron's formula, which computes the area of a triangle given its side ...

  8. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    Heron of Alexandria found what is known as Heron's formula for the area of a triangle in terms of its sides, and a proof can be found in his book, Metrica, written around 60 CE.

  9. Descartes' theorem - Wikipedia

    en.wikipedia.org/wiki/Descartes'_theorem

    Additional proofs involve arguments based on symmetry, calculations in exterior algebra, or algebraic manipulation of Heron's formula (for which see § Soddy circles of a triangle). [22] [23] The result also follows from the observation that the Cayley–Menger determinant of the four coplanar circle centers is zero. [24]