Geometrical models of quadratic-rectangular sets with particular examples of composite solutions

During the current decades the aspect of geometrography compositions formation on the basis of basic images has been actively developed. The basic images possess the qualities of harmonies, expressed by lines, squares, tone, color. The relations of square-rectangular forms belonging to plane geometr...

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Main Authors: Polezhaev Yuriy Olegovich, Borisova Anzhelika Yur'evna, Borisova Viktoria Aleksandrovna
Format: Article
Language:English
Published: Moscow State University of Civil Engineering (MGSU)
Series:Vestnik MGSU
Subjects:
Online Access:http://vestnikmgsu.ru/files/archive/issues/2014/9/ru/18.pdf
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spelling doaj-6c6e87d0f4294efdb62d29c191297f342020-11-24T21:27:53ZengMoscow State University of Civil Engineering (MGSU)Vestnik MGSU 1997-09359161167Geometrical models of quadratic-rectangular sets with particular examples of composite solutionsPolezhaev Yuriy Olegovich0Borisova Anzhelika Yur'evna1Borisova Viktoria Aleksandrovna2Moscow State University of Civil Engineering (MSUCE)Moscow State University of Civil Engineering (MSUCE)Moscow State University of Civil Engineering (MGSU)During the current decades the aspect of geometrography compositions formation on the basis of basic images has been actively developed. The basic images possess the qualities of harmonies, expressed by lines, squares, tone, color. The relations of square-rectangular forms belonging to plane geometry of parabolic, hyperbolic and elliptic fields has been already analyzed by scientists. This article introduces equiareals construction of square-rectangular shapes, as well as their rows - in classical composition of elementary figures of "squaring the circle". Variations of such constructions, in their turn, offer the possibility to seek and capture new geometrical graphical compositions, practical application of which can be wide enough in technology design and mechanical engineering, architecture and construction, decoration of household items, arts and crafts and costume fabrics, et cetera. The authors consider the topic of plane geometry "Field-M", which is based on a rectilinear grid of ortholines with circulations in its nodal points. The conclusions made by the authors is that the necessity of solutions for more and more various and complicated problems in the conditions of time limitation determines the development of geometrography methods as an effective operating system along with program methods of cognitive graphics.http://vestnikmgsu.ru/files/archive/issues/2014/9/ru/18.pdfplanimetryhomothetycircularequiarealsortholines"running point"incidencesquaring the circlechordellipse
collection DOAJ
language English
format Article
sources DOAJ
author Polezhaev Yuriy Olegovich
Borisova Anzhelika Yur'evna
Borisova Viktoria Aleksandrovna
spellingShingle Polezhaev Yuriy Olegovich
Borisova Anzhelika Yur'evna
Borisova Viktoria Aleksandrovna
Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
Vestnik MGSU
planimetry
homothety
circular
equiareals
ortholines
"running point"
incidence
squaring the circle
chord
ellipse
author_facet Polezhaev Yuriy Olegovich
Borisova Anzhelika Yur'evna
Borisova Viktoria Aleksandrovna
author_sort Polezhaev Yuriy Olegovich
title Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
title_short Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
title_full Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
title_fullStr Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
title_full_unstemmed Geometrical models of quadratic-rectangular sets with particular examples of composite solutions
title_sort geometrical models of quadratic-rectangular sets with particular examples of composite solutions
publisher Moscow State University of Civil Engineering (MGSU)
series Vestnik MGSU
issn 1997-0935
description During the current decades the aspect of geometrography compositions formation on the basis of basic images has been actively developed. The basic images possess the qualities of harmonies, expressed by lines, squares, tone, color. The relations of square-rectangular forms belonging to plane geometry of parabolic, hyperbolic and elliptic fields has been already analyzed by scientists. This article introduces equiareals construction of square-rectangular shapes, as well as their rows - in classical composition of elementary figures of "squaring the circle". Variations of such constructions, in their turn, offer the possibility to seek and capture new geometrical graphical compositions, practical application of which can be wide enough in technology design and mechanical engineering, architecture and construction, decoration of household items, arts and crafts and costume fabrics, et cetera. The authors consider the topic of plane geometry "Field-M", which is based on a rectilinear grid of ortholines with circulations in its nodal points. The conclusions made by the authors is that the necessity of solutions for more and more various and complicated problems in the conditions of time limitation determines the development of geometrography methods as an effective operating system along with program methods of cognitive graphics.
topic planimetry
homothety
circular
equiareals
ortholines
"running point"
incidence
squaring the circle
chord
ellipse
url http://vestnikmgsu.ru/files/archive/issues/2014/9/ru/18.pdf
work_keys_str_mv AT polezhaevyuriyolegovich geometricalmodelsofquadraticrectangularsetswithparticularexamplesofcompositesolutions
AT borisovaanzhelikayurevna geometricalmodelsofquadraticrectangularsetswithparticularexamplesofcompositesolutions
AT borisovaviktoriaaleksandrovna geometricalmodelsofquadraticrectangularsetswithparticularexamplesofcompositesolutions
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