IJAM: Volume 37, No. 2 (2024)

DOI: 10.12732/ijam.v37i2.4

 

ON THE GEOMETRIC PROPERTIES

OF THE MINKOWSKI OPERATOR

 

Mashrabjon Mamatov 1 , Jalolxon Nuritdinov 2, §

 

1 Department of Geometry and Topology

of National University of Uzbekistan

Tashkent - 100174, UZBEKISTAN

2 Department of Digital Technologies and

Mathematics of Kokand University

Kokand - 150700, UZBEKISTAN

 

Abstract.  This article is about Minkowski difference of sets, which is one of the Minkowski operators. The necessary and sufficient conditions for the existence of the Minkowski difference of given regular polygons in the plane are derived. The method of finding the Minkowski difference of given regular tetrahedrons in the Euclidean space R3 is explained. Results for finding the Minkowski difference of given n-dimensional cubes in space Rn are also presented.

 

At the end of the article, the obtained results are summarized and a geometric method for finding the Minkowski difference of the convex set M and compact set N given in Rn is shown. The theory of foliations is applied to find the Minkowski difference of sets. New geometric concepts such as “dense embedding” and “completely dense embedding” are introduced. An important

geometric property of the Minkowski operator is introduced and proved as a theorem.

 

 

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How to cite this paper?
DOI: 10.12732/ijam.v3
7i2.4
Source: 
International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 202
4
Volume: 3
7
Issue: 2

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