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A gravimeter measures this gravitational force. For a small body, general relativity predicts gravitational effects indistinguishable from the effects of acceleration by the equivalence principle. Thus, gravimeters can be regarded as special-purpose accelerometers. Many weighing scales may be regarded as simple
He invented the calculus of variations and formulated the Euler–Lagrange equation for reducing optimization problems in this area to the solution of differential equations. Euler pioneered the use of analytic methods to solve number theory problems.
L in equation (1) above was the length of an ideal mathematical 'simple pendulum' consisting of a point mass swinging on the end of a massless cord. However the 'length' of a real pendulum, a swinging rigid body, known in mechanics as a compound pendulum , is more difficult to define.
Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been determined as a unique compound, that known measurement can then be used to determine the same analyte's mass in a mixture, as long as the relative ...
During antiquity and the medieval periods, bursts of mathematical creativity were often followed by centuries of stagnation. As the early modern age opened and the worldwide spread of knowledge began, written examples of mathematical developments came to light. Symbolic stage—where comprehensive systems of notation supersede rhetoric. The ...
The equation for universal gravitation thus takes the form: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses , and G is the gravitational constant .
William Thomson, 1st Baron Kelvin (26 June 1824 – 17 December 1907 [7]), was a British mathematician, mathematical physicist and engineer. [8] [9] Born in Belfast, he was the professor of Natural Philosophy at the University of Glasgow for 53 years, where he undertook significant research and mathematical analysis of electricity, was instrumental in the formulation of the first and second ...
The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing thextraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers (London, 1557). This was the book in which the equals sign was introduced within a printed edition. [6]