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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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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