Brahmagupta's formula

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	Final Project
		Because Brahmagupta's Generalization works only for cyclic quadrilaterals, it is interesting to note that an extension of his formula can be used to find the area of any quadrilateral.
		The formula is often called Brahmagupta's Generalization, as opposed to Brahmagupta's Formula, because later commentators assumed it was a formula to be used to find the area of any quadrilateral.
		This extension of Brahmagupta's Generalization then reduces to Heron's Formula.
	jwilson.coe.uga.edu /EMT668/EMAT6680.2000/Umberger/MATH7200/HeronFormulaProject/finalproject.html (964 words)

	Mathwords Page 12
		The formula of Brahmagupta extends the Heron method by reducing the semi-perimeter, s, by each of the four sides. In this way Heron's formula can be thought of as a special case of a cyclic quadrilateral when one side is diminished to zero to form a triangle.
		The s in Brahmagupta's method, like Heron's, is one half the perimeter of the figure, s = (a+b+c+d)/2. The formula for the area of a cyclic quadrilateral,
		The Indian Mathematician Brahmagupta (598-670) is often claimed to be the greatest mathematician of the dark ages.
	www.pballew.net /arithm12.html (3982 words)

	Brahmagupta
		Of particular interest to mathematics in this second work by Brahmagupta is the interpolation formula he uses to compute values of sines.
		Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time.
		Brahmagupta believed in a static Earth and he gave the length of the year as 365 days 6 hours 5 minutes 19 seconds in the first work, changing the value to 365 days 6 hours 12 minutes 36 seconds in the second book the Khandakhadyaka.
	zyx.org /Brahmagupta.html (1400 words)

	PlanetMath: Brahmagupta's formula
		This is version 3 of Brahmagupta's formula, born on 2001-10-06, modified 2001-10-31.
	planetmath.org /encyclopedia/BrahmaguptasFormula.html (20 words)

	Heron's Formula and Brahmagupta's Generalization
		For a cyclic quadrilateral the each pair of opposite angles sums to pi, so it reduces to Brahmagupta's formula.
		Brahmagupta didn't actually give a formal proof of this result, and in fact the surviving copies of his statement of this proposition don't mention the fact that it applies only to cyclic quadrilaterals.
		It's tempting to think that Brahmagupta might have just imagined the equation based on its formal symmetry.
	www.mathpages.com /home/kmath196.htm (512 words)

	Brahmagupta's Formula for the Area of a Cyclic Quadrilateral
		Brahmagupta's formula is provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle) with sides of length a, b, c, and d as
		Consider Brahmagupta's formula as one side, say the one of length d wnlog, varies and approaches zero in length.
		Use Brahmagupta's formula to develop equations for the length of the two diagonals of the quadrilateral.
	jwilson.coe.uga.edu /emt725/brahmagupta/brahmagupta.html (414 words)

	Brahmagupta's Theorem
		Brahmagupta was a Hindu mathematician of the seventh century AD who discovered a neat formula for the area of a cyclic quadrilateral.
		But it is possible to prove that if a cyclic quadrilateral has perpendicular diagonals crossing at P, the line through P perpendicular to any side bisects the opposite side.
	www.mth.uct.ac.za /digest/brahmagupta.html (104 words)

	Brahmagupta's Formula
		Brahmagupta's formula provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle) with sides of length a, b, c, and d as
		Having shown Brahmagupta's formula true for rectangles, we assume this cyclic quadrilateral is not a rectangle, so WLOG we assume AB and CD are not parallel.
		Brahmagupta first published this result in 628 in a book that included many other groundbreaking mathematical results.
	mcraefamily.com /MathHelp/GeometryCyclicQuadrilateralBrahmagupta.htm (460 words)

	Social Science
		The University of Virginia's site has some examples of the formulas Brahmagupta wrote.
		Brahmagupta was one of the leading mathematicians of the ancient world and wrote important works in math and astronomy.
		If the perimeter of a quadrilateral is the sum of the lengths of its four sides -- a, b, c, and d -- write a formula to calculate the perimeter of a quadrilateral.
	www.mathsurf.com /8/ch3/social (95 words)

	did you know?
		To Brahmagupta he pays homage at the beginning of his Siddhanta-siromani and most of his astronomical elements are taken from the Brahmasphuta siddhanta or the Rajamrganka belonging to the same school.
		After criticising Brahmagupta's rule for finding the diagonals of quadrilaterals, he gives his method of getting a rational quadrilateral by the juxtaposition of rational right triangles and shows how the diagonals are then easily found.
		Circles are dealt with next, a very satisfactory approximate formula for calculating the arc in terms of the chord and vice versa were given, so also are given the correct expressions for the volume and surface of a sphere.
	www.infinityfoundation.com /mandala/t_dy/t_dy_Q13.htm (1909 words)

	A Proof of the Pythagorean Theorem From Heron's Formula
		For a quadrilateral with sides a, b, c and d inscribed in a circle there exists a generalization of Heron's formula discovered by Brahmagupta.
	www.cut-the-knot.org /pythagoras/herons.shtml (230 words)

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