Indian mathematicians brahmagupta biography of william shakespeare

B Datta, Brahmagupta, Bull. Calcutta Math. XII Wiesbaden,83 - R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math. Education 8B 33 -B R C Gupta, Brahmagupta's rule for the volume of frustum-like solids, Math. Education 6B -B S Jha, A critical study on 'Brahmagupta and Mahaviracharya and their contributions in the field of mathematics', Math.

Siwan 12 466 - T Kusuba, Brahmagupta's sutras on tri- and quadrilaterals, Historia Sci. J Pottage, The mensuration of quadrilaterals and the generation of Pythagorean triads : a mathematical, heuristical and historical study with special reference to Brahmagupta's rules, Arch. History Exact Sci. Additional Resources show. Honours show.

Additionally he introduced the concept of negative numbers. Brahmagupta argued that the Earth and the universe are round and not flat. He was the first to use mathematics to predict the positions of the planets, the timings of the lunar and solar eclipses.

Indian mathematicians brahmagupta biography of william shakespeare

Though all this seems like obvious and simple solutions it was a major improvement in science at that time. This great mathematician died between and He was one of the greatest mathematicians in Indian history and his contributions to mathematics and science have made major differences to various mathematical problems by establishing the basic rules which now allow us to find their solutions.

This is nice. I am currently working on a paper for my college algebra class. Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area. The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral.

The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral. Although Brahmagupta does not explicitly state that these quadrilaterals are cyclic, it is apparent from his rules that this is the case. Brahmagupta dedicated a substantial portion of his work to geometry.

One theorem gives the lengths of the two segments a triangle's base is divided into by its altitude:. The indian mathematicians brahmagupta biography of william shakespeare decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular [altitude] is the square-root from the square of a side diminished by the square of its segment.

He further gives a theorem on rational triangles. A triangle with rational sides abc and rational area is of the form:. The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular [altitudes].

He continues to give formulas for the lengths and areas of geometric figures, such as the circumradius of an isosceles trapezoid and a scalene quadrilateral, and the lengths of diagonals in a scalene cyclic quadrilateral. This leads up to Brahmagupta's famous theorem. Imaging two triangles within [a cyclic quadrilateral] with unequal sides, the two diagonals are the two bases.

Their two segments are separately the upper and lower segments [formed] at the intersection of the diagonals. The two [lower segments] of the two diagonals are two sides in a triangle; the base [of the quadrilateral is the base of the triangle]. Its perpendicular is the lower portion of the [central] perpendicular; the upper portion of the [central] perpendicular is half of the sum of the [sides] perpendiculars diminished by the lower [portion of the central perpendicular].

The diameter and the square of the radius [each] multiplied by 3 are [respectively] the practical circumference and the area [of a circle]. The accurate [values] are the square-roots from the squares of those two multiplied by ten. After giving the value of pi, he deals with the geometry of plane figures and solids, such as finding volumes and surface areas or empty spaces dug out of solids.

He finds the volume of rectangular prisms, pyramids, and the frustum of a square pyramid. He further finds the average depth of a series of pits. For the volume of a frustum of a pyramid, he gives the "pragmatic" value as the depth times the square of the mean of the edges of the top and bottom faces, and he gives the "superficial" volume as the depth times their mean area.

The sines: The Progenitors, twins; Ursa Major, twins, the Vedas; the gods, fires, six; flavors, dice, the gods; the moon, five, the sky, the moon; the moon, arrows, suns [ Here Brahmagupta uses names of objects to represent the digits of place-value numerals, as was common with numerical data in Sanskrit treatises. Progenitors represents the 14 Progenitors "Manu" in Indian cosmology or 14, "twins" means 2, "Ursa Major" represents the seven stars of Ursa Major or 7, "Vedas" refers to the 4 Vedas or 4, dice represents the number of sides of the traditional die or 6, and so on.

In Brahmagupta devised and used a special case of the Newton—Stirling interpolation formula of the second-order to interpolate new values of the sine function from other values already tabulated. The earth on all its sides is the same; all people on the earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow If a thing wants to go deeper down than the earth, let it try.

The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth. The division was primarily about the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta's case, the disagreements stemmed largely from the choice of astronomical parameters and theories.

If the moon were above the sun, how would the power of waxing and waning, etc. The near half would always be bright. In the same way that the half seen by the sun of a pot standing in sunlight is bright, and the unseen half dark, so is [the illumination] of the moon [if it is] beneath the sun. The brightness is increased in the direction of the sun.

At the end of a bright [i. Hence, the elevation of the horns [of the crescent can be derived] from calculation. He explains that since the Moon is closer to the Earth than the Sun, the degree of the illuminated part of the Moon depends on the relative positions of the Sun and the Moon, and this can be computed from the size of the angle between the two bodies.

Further work exploring the longitudes of the planets, diurnal rotation, lunar and solar eclipses, risings and settings, the moon's crescent and conjunctions of the planets, are discussed in his treatise Khandakhadyaka. Contents move to sidebar hide. Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version. In other projects.

Wikimedia Commons Wikisource Wikidata item. This is the latest accepted revisionreviewed on 4 January Indian mathematician and astronomer — Rules for computing with Zero Modern numeral system Brahmagupta's theorem Brahmagupta's identity Brahmagupta's problem Brahmagupta—Fibonacci identity Brahmagupta's interpolation formula Brahmagupta's formula.

In this work, Brahmagupta advanced novel ideas and algorithms for various celestial phenomena, including eclipses, planetary positions, and timekeeping. The mathematical chapters of the Brahamasphutasiddhanta demonstrate Brahmagupta's expertise in arithmetic, algebra, and geometry. His work laid the foundation for the development of algebra in subsequent centuries.

Brahmagupta's work was translated into Arabic under the patronage of the Abbasid caliph al-Mansur in the 8th century. This translation, known as the "Great Sindhind," had a profound impact on Islamic scholars such as al-Khwarizmi and al-Battani.