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Because the "sweep" of the area under the involute is bounded by a tangent line (see diagram and derivation below) which is not the boundary (¯) between overlapping areas, the decomposition of the problem results in four computable areas: a half circle whose radius is the tether length (A 1); the area "swept" by the tether over an angle of 2 ...
The region connection calculus (RCC) is intended to serve for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidean space, or in a topological space) by their possible relations to each other. RCC8 consists of 8 basic relations that are possible between two regions: disconnected (DC) externally ...
Calculus is also used to gain a more precise understanding of the nature of space, time, and motion. For centuries, mathematicians and philosophers wrestled with paradoxes involving division by zero or sums of infinitely many numbers. These questions arise in the study of motion and area.
The following is a proof of half of the theorem for the simplified area D, a type I region where C 1 and C 3 are curves connected by vertical lines (possibly of zero length). A similar proof exists for the other half of the theorem when D is a type II region where C 2 and C 4 are curves connected by horizontal lines (again, possibly of zero ...
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
The idea originated in the late 5th century BC with Antiphon, although it is not entirely clear how well he understood it. [1] The theory was made rigorous a few decades later by Eudoxus of Cnidus, who used it to calculate areas and volumes. It was later reinvented in China by Liu Hui in the 3rd century AD in order to find the area of a circle. [2]
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