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Brahmagupta initiated a new branch of Mathematics, Interpolation theory. When he was 67 years old, Brahmagupta, as mentioned earlier, wrote another Expository astronomical book called “Khandakhadyaka” in ad 665. In Chapter IX of this book, he introduces a new method of obtaining from a given table of sines consisting of tabulated values of ...
Feb 1, 2010 · Abstract. This paper shows that Propositions XII.21–27 of Brahmagupta’s Br a hmasphuṭasiddh a nta (628 a.d.) constitute a coherent mathematical discourse leading to the expression of the area of a cyclic quadrilateral in terms of its sides. The radius of the circumcircle is determined by considering two auxiliary quadrilaterals.
Nov 1, 2012 · Brahmagupta states that the portions determined by the intersection of perpendiculars with each of the two (produced) diagonals may be determined: for the lower portions, one should use proportion (anupāta) as in XII.25; for the upper ones, one should subtract the lower portion from the full perpendicular. Therefore, the full perpendiculars should also be determined.
Brahmagupta was very well acquainted with the mathematics and astronomy of Aryabhata I. He seems to criticize Aryabhata I severely in his work “Brahma Sphuta Siddhanta” but seems to be compelled to bow to Aryabhata’s popularity by referring to Aryabhata with tremendous reverence in his later work, “Khandakadyaka.”
Jul 1, 2023 · River bankline migration is a frequent phenomenon in the river of the floodplain region. Nowadays, channel dynamics-related changes in land use and la…
Jan 1, 2008 · Any Brahmagupta quadrilateral with four integer sides has integer area and even perimeter. Proof. Since the sides are integral and the area is rational, then (4K 4 ) 2 = 8abcd + 2 parenleftbig a 2 b 2 + a 2 c 2 + a 2 d 2 + b 2 c 2 + b 2 d 2 + c 2 d 2 parenrightbig − a 4 − b 4 − c 4 − d 4 implies that 4K 4 ∈ Z.
Description. Mathematics in India has a long and impressive history. Presented in chronological order, this book discusses mathematical contributions of Pre-Modern Indian Mathematicians from the Vedic period (800 B.C.) to the 17 th Century of the Christian era. These contributions range across the fields of Algebra, Geometry and Trigonometry.
Aug 1, 2016 · On the whole, Colebrooke allegedly misinterpreted the geometrical part of Brahmagupta's, and even Bhāskara's, work, because he was looking for “elements of geometry” of some kind, and therefore only paid heed to “a few elementary and primary propositions, upon which all of Hindu science [presumably] rested”. 112 This bias in return induced the view that “they (the Hindus) cultivated Algebra much more, and with greater success, than Geometry; as is [purportedly] evident from the ...
Aug 1, 1978 · This ‘proof’ of the theorem is also found in Bhaskara II's work in the 12th century A.D., giving rise to the question of possible transmission. Finally, this paper surveys Chinese interest in right-angled and similar triangles in three other old Chinese texts, namely, the Chiu-chang suan-shu, Hai-tao suan-ching and Chang Ch'iu-chien suan ...
Isosceles triangle. In subject area: Mathematics. i.e., “In an isosceles triangle, the sum of the squares of two unequal rational numbers is the side, twice the difference of the squares of the two unequal numbers is the base and twice the product of the two unequal numbers is the altitude.”. From: Mathematical Achievements of Pre-Modern ...
