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Basic Mathematical Calculations for Data Analytics
Published in Adedeji B. Badiru, Data Analytics, 2020
A circular torus is formed by the rotation of a circle about an axis in the plane of the circle and not cutting the circle. Let r be the radius of the revolving circle and R be the distance of its center from the axis of rotation. S=4π2RrV=2π2Rr2
Topological Analysis of Local Structure in Atomic Systems
Published in Jeffrey P. Simmons, Lawrence F. Drummy, Charles A. Bouman, Marc De Graef, Statistical Methods for Materials Science, 2019
Emanuel A. Lazar, David J. Srolovitz
Topology is the mathematical study of properties of objects that do not change under continuous deformations; these properties are often related to the manner in which objects are connected to themselves and to other objects. To illustrate this idea, consider the shapes shown in Figure 15.5. While the sphere can be continuously deformed into the ellipsoid without cutting or gluing, the torus cannot. In the language of topology, the sphere and ellipsoid are isomorphic with one another, whereas the torus is not isomorphic to either.
General introduction
Published in Adedeji B. Badiru, Handbook of Industrial and Systems Engineering, 2013
A circular torus is formed by the rotation of a circle about an axis in the plane of the circle and not cutting the circle. Let r be the radius of the revolving circle and let R be the distance of its center from the axis of rotation. S=4π2RrV=2π2Rr2
An adaptive process of reverse engineering from point clouds to CAD models
Published in International Journal of Computer Integrated Manufacturing, 2020
A torus is given by its axis , the center , the major radius and the minor radius .