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Vol 39 Iss. 3
Pages:
95-106
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RUS
Article

Depiction of images of multidimensional spaces by orthogonal projections of vectors

Authors:
P. V. Filippov
Date submitted:
1960-09-07
Date accepted:
1960-11-14
Date published:
1961-09-12

Abstract

The methods of projective geometry make it possible to use numerous geometric systems, which is widely used in the works of E. S. Fedorov. At present, even in the educational manuals on projective geometry do not mention the existence of various geometric systems, which, however, open wide opportunities for solving a number of problems of engineering and scientific practice.

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References

  1. Fedorov E. S. New Geometry as a Basis for Drawing. SPb, 1907.
  2. Fedorov E. S. Accurate representation of points of space on the plane. Journal of Mining Institute, vol. I, iss. 1, 1908.
  3. Fedorov E. S. Basic features of the new geometry. Journal of Mining Institute, vol. III, vol. 5, 1912.
  4. Fedorov E. С. A simple and accurate representation of points of space of four dimensions in the plane by means of vectors. Journal of Mining Institute, vol. II, iss. 3, 1909.
  5. Fedorov E. С. Graphical operations with four independent variables. Proc. of the Russian Academy of Sciences, Series VI, No. 7, 1918.
  6. Fedorov E. S. Linear sets of vectors in space. Journal of Mining Institute, vol. V, iss. 1, 1914.
  7. Lodochnikov V. N. The simplest ways of depicting multicomponent systems. Proc. of the Institute of Physico-Chemical Analysis, vol. II, iss. 2, 1924,
  8. Shishokin V. P. Analytical and Graphical Methods of Investigation of Complex Equilibrium Systems. Proc. of the Institute of Physico-Chemical Analysis, vol. III, iss. 1, 1926.
  9. Pryanishnikova Z. I. Generalization of E. S. Fedorov's projections. Collection. Methods of Descriptive Geometry and its Applications. GITTL, 1955.
  10. Zhitomirskiy O. K. Projective geometry in tasks. GITTL, 1954.
  11. Rocke N. E. New Yearbook of Mineralogy, 1916, v. II, p. 109.
  12. Schoute P. H. Multidimensional geometry. V. I. Leipzig, 1902.

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