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# A Survey of the Discoveries of Calculations and Methods to Do Mathematical Calculations

Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay This dilemma can be solved by calculus which helps determine the rate of decay of the radioactive material Calculus can aid people in many everyday situations such as deciding how much fencing is needed to encompass a designated area Finding how gravity affects certain objects is how calculus aids people who study Physics Mechanics find calculus useful to determine rates of flow of fluids in a car Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus which is still expandingThe first mathematicians came from Egypt where they discovered the rule for the volume of a pyramid and approximation of the area of a circle Later Greeks made tremendous discoveries Archimedes extended the method of inscribed and circumscribed figures by means of heuristic which are rules that are specific to a given problem and can therefore help guide the search These arguments involved parallel slices of figures and the laws of the lever the idea of a surface as made up of lines Finding areas and volumes of figures by using conic section a circle point hyperbola etc and weighing infinitely thin slices of figures an idea used in integral calculus today was also a discovery of Archimedes One of Archimedess major crucial discoveries for integral calculus was a limit that allows the slices of a figure to be infinitely thin Another Greek Euclid developed ideas supporting the theory of calculus but the logic basis was not sustained since infinity and continuity werent established yet Boyer 47 His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points lines or surfaces but by the limit of an infinite sequence Boyer 47 These early discoveries aided Newton and Leibniz in the development of calculusIn the 17th century people from

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