# Vestnik КRAUNC. Fiz.-Mat. nauki. 2024. vol. 46. no. 1. P. 22-51. ISSN 2079-6641

MATHEMATICS
https://doi.org/10.26117/2079-6641-2024-46-1-22-51
Research Article
Full text in Russian
MSC 97G40

Contents of this issue

On the New Problems in Stereometry

\fbox{\bf B. P. Fedorov} , S. B. Bogdanova^\ast, S. O. Gladkov

Moscow Aviation Institute, 125993, Moscow, Volokolamskoe sh., 4, Russia

Abstract. It were given original combinative problems with regular polyhedrons, which including well-known tetrahedrons and cubes, and also the lesser-known octahedrons, dodecahedrons and icosahedrons due to its complexity. The solution of the problem of the calculation of the edge of octahedron, dodecahedron and icosahedron by using the the side of inscribed and circumscribed cubes has been given. The radius of the circumsphered circle and midsphere around the dodecahedron and icosahedron has been calculated. Two triangular pyramids and two tetragonal ones, as well as the triangular pyramid with a cone have been arranged. In the second chapter of the paper, it were shown several non-trivial combinations of the bodies with a common vertex, in which the height of one body was a lateral edge of the other one and in which the volume of generalities bodies was found. Two triangular pyramids and two tetragonal ones, as well as the triangular pyramid with a cone have been arranged. Each problem was going with the detailed figure, and the solution to the problems with Platon body was including several supporting ones as well. This paper could be used by high school mathematics teachers not only as methodological support, but also as a clear example in preparation for the Olympiad tasks in math for students.

Key words: regular bodies, Euler ratio, Euclid’s theorem, angular defect, aggregates and crosscuts of the
bodies.

Received: 16.01.2024; Revised: 25.02.2024; Accepted: 27.02.2024; First online: 07.03.2024

For citation. Fedorov B.P. , Bogdanova S. B., Gladkov S. O. On the new problems in stereometry. Vestnik KRAUNC. Fiz.-mat. nauki. 2024, 46: 1, 22-51. EDN: PSNZPU. https://doi.org/10.26117/2079-6641-2024-46-1-22-51.

Funding. The work was not carried out within the framework of funds
Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^astCorrespondence: E-mail: sonjaf@list.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Institute of Cosmophysical Research and Radio Wave Propagation, 2024 (original layout, design, compilation)

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