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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 · As a result, Brahmagupta’s formula is to be found in most textbooks on the history of mathematics. 5 The contemporary reaction to Colebrooke’s translation is summarized by Chasles [1837, 429]: “This formula for the area of the triangle as a function of the sides, has been noticed in Brahmagupta’s work, by the geometers who reported on it, and has been regarded as the most considerable proposition in it; and one has never quoted, I think, the formula for the area of the quadrilateral.
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…
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.
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.
Nov 1, 1997 · Abstract. This paper gives both a new interpretation of Āryabha t · a's rule for sine-differences prescribed in the second chapter of his Āryabha t · ı̄ya (A.D. 499/510), one of the oldest astronomical texts in India, and a hypothesis about the origin of his table of sine-differences given in the first chapter of the same work.
Dec 1, 2022 · In particular, in Section 2 we will study a generalization of the group structure on Pell hyperbolas defined by the equation x 2 − d y 2 = c, writing the group operation in terms of Brahmagupta products and providing an explicit isomorphism with the classical Pell hyperbolas. In Section 3, we will provide a parameterization for Pell hyperbolas exploiting an algebraic approach and connecting it also to a geometrical interpretation.
Jan 1, 1991 · In A.D. 1100, Al-Beruni named five known Siddanthas: (1) Brahma Siddantha which was named after the Spiritual Being, Brah- man, and composed by Brahmagupta. (2) Vasishta Siddantha named after a star in the Great Bear constellation, or perhaps after a great teacher, Vasishta and composed by Vishnuchandra.
