Obtaining of Four-Dimensional Nomograms Based on Similarity Theorem

Yu. Levkin

doi:doi:10.12737/article_5953f334279642.78930109

UDC 51

Obtaining of Four-Dimensional Nomograms Based on Similarity Theorem

Published в Geometry & Graphics · Volume 5, Issue 2, 2017 · Pages 69–74 · Rubrics: Scientific problems of geometry

DOI 10.12737/article_5953f334279642.78930109

Received: 28.06.2017 Accepted: 04.07.2017 Published: 04.07.2017 Language of publication: RUS

Authors

Yu. Levkin ¹

1 Tolyatti State University (kafedra «Nachertatel'naya geometriya», Senior Lecturer)
Samara, Samara, Russian Federation

ABSTRACT

In some performed experimental works there is no total characteristic of study processes with regard to their physical understanding. It’s possible to achieve such understanding by means of epure and graphic interdependency for parameters illustrating experiment process, and by means of geometrical images which testify regularity of their outline, and are characteristic of physical process. The use of epure multidimensional octant nomogram can promote the solution for a number of application-oriented problems. By means of two octant epure nomograms constructed on experimental tabular data with four or five parameters, the optimum choice of graphic execution and its implementation in the area of physical genesis is offered. This method’s justifications have been given in the paper. A basis for extension of new opportunities is certainly descriptive geometry that facilitates a solution to technical tasks on multidimensional geometry. At the heart of similarity of adjacent octant cells with general axis are plotted two octant axonometric nomograms creating interdependencies between parameters by means of communication lines. This method opens a possibility for physical processes’ nature understanding. In this paper have been presented two graphic models for two octant nomograms in which advantages of their creation and reading have been presented. Foundations on which derivations are built when constructing the nomograms are validated by the similarity theorem and the axiom of projected surface. Absolute values of parameters are actual ones, and presented from papers of journals, as well as from peer-reviewed scientific publications recommended by Higher Attestation Commission.

KEYWORDS

descriptive geometry multi-component systems spatial nomography functional and reasoning axes communication lines experiment’s physical component working horizontal plane reasoning frontal plane reasoning profile plane similarity theorem axonometric projections octant nomograms two-octant nomogram coordinate axes.

Information Text References

Authors:

1. Tolyatti State University (kafedra «Nachertatel'naya geometriya», Senior Lecturer)

Samara, Samara, Russian Federation

Type:

Article

Pages:

from 69 to 74

Status:

Published

Subject area:

UDC 51

Language:

Russian, English

Keywords:

descriptive geometry, multi-component systems, spatial nomography, functional and reasoning axes, communication lines, experiment’s physical component, working horizontal plane, reasoning frontal plane, reasoning profile plane, similarity theorem, axonometric projections, octant nomograms, two-octant nomogram, coordinate axes.

Text

В 1906–1908 гг. впервые в Росси начал заниматься вопросами номографии Н.М. Герсеванов. Большая заслуга в деле развития теории номограмм и организации номографирования инженерных расчетов принадлежит Н.А. Глаголеву, возглавившему советскую номографическую школу [2].

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