Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F13%3A%230000993" target="_blank" >RIV/46747885:24510/13:#0000993 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.4854736" target="_blank" >http://dx.doi.org/10.1063/1.4854736</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4854736" target="_blank" >10.1063/1.4854736</a>

Result language
angličtina
Original language name
Alternative Method for Calculations of Volumes by Using Parameterizations Surfaces Areas
Original language description
The paper presents an alternative general method for calculations of areas (respective volumes) of n-dimensional solids in Euclidean space, where calculations of volumes are based on knowledge of suitable descriptions of surfaces areas of their bodies. The problem is investigated as to be topological. The method deals with bounded and (piecewise) smooth hypersurfaces in E n . Applying the alternative theory in E 2 , we have got the corollary of Green's theorem for the curvilinear integral. In E 3 , it is Gauss-Ostrogradsky Theorem (The Divergence Theorem) presenting a relationship between the flux of a vector field by a closed simply connected smooth area and a surface integral of the divergence of that vector field over the volume closed by that surface. This contribution consists of the proof of the theory and examples of volumes of special solids.
Czech name
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Czech description
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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