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Here Brahmagupta found the result in terms of the sum of the first n integers, rather than in terms of n as is the modern practice. [24] He gives the sum of the squares of the first n natural numbers as n(n + 1)(2n + 1) / 6 and the sum of the cubes of the first n natural numbers as ( n(n + 1) / 2 ) 2.
Brahmagupta (c. 598 – c. 668 AD) was the first Indian scholar to describe gravity as an attractive force: [38] [39] [failed verification] [40] [41] [failed verification] 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 ...
Brāhmasphuṭasiddhānta is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zero. [4] For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive.
The formulation of Newtonian gravity in terms of a gravitational constant did not become standard until long after Cavendish's time. Indeed, one of the first references to G is in 1873, 75 years after Cavendish's work. [20] Cavendish expressed his result in terms of the density of the Earth.
The book begins its first chapter by discussing ancient history and old beliefs regarding gravity and what lies above. This includes a discussion of belief in gods and how those religious views were shaped by the existence of gravity and its prevalence on living beings and all matter. [1]
The book that educated at least two generations of researchers in gravitational physics. Comprehensive and encyclopedic, the book is written in an often-idiosyncratic way that you will either like or not. Pankaj Sharan writes: [7] This large sized (20cm × 25cm), 1272 page book begins at the very beginning and has everything on gravity (up to ...
1911 – Max von Laue publishes the first textbook on special relativity. [52] 1911 – Albert Einstein explains the need to replace both special relativity and Newton's theory of gravity; he realizes that the principle of equivalence only holds locally, not globally. [53] 1912 – Friedrich Kottler applies the notion of tensors to curved ...
Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced by Élie Cartan in 1923 [1] [2] and Kurt Friedrichs [3] and later developed by G. Dautcourt, [4] W. G. Dixon, [5] P. Havas, [6] H. Künzle, [7] Andrzej Trautman, [8] and others. [9]