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Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)

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Geometric Figures Which Appear After VV Cutting in the Radial Cross Section of Generalized Möbius-Listing Bodies
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Authors
Ilia Tavkhelidze1, *
1
Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi, Georgia
*
Corresponding author. Email: ilia.tavkhelidze@tsu.ge
Corresponding Author
Ilia Tavkhelidze
Article History
Received 20 August 2023
Revised 29 August 2023
Accepted 5 October 2023
Available Online 29 November 2023
DOI
https://doi.org/10.55060/s.atmps.231115.004
Keywords
Analytic representation
Möbius-Listing bodies
Cutting of GML bodies
Abstract

In previous works we were able to calculate all possible outcomes, and various options that appear, after VV, VS or SS cuts of GML bodies with the help of so-called straight chordal knives. Then we did not specify how many and what types of planar figures appear on the radial cross section of the GMLmn body, depending on 1) m: the number of polygon vertices, 2) n: the number of twists, which also is a parameter showing which vertices (sides) are connected by this knife. In this article, a regularity is reported that allows to calculate the number and nature of planar figures appearing after an arbitrary VV in arbitrary regular m-gon. This work is another step towards solving the question whether it is possible to unequivocally restore the GML body knowing the information about the traces left on the radial cross section.

Copyright
© 2023 The Authors. Published by Athena International Publishing B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/).
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Cite This Article

ris 
TY  - CONF
AU  - Ilia Tavkhelidze
PY  - 2023
DA  - 2023/11/29
TI  - Geometric Figures Which Appear After VV Cutting in the Radial Cross Section of Generalized Möbius-Listing Bodies
BT  - Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022)
PB  - Athena Publishing
SP  - 41
EP  - 45
SN  - 2949-9429
UR  - https://doi.org/10.55060/s.atmps.231115.004
DO  - https://doi.org/10.55060/s.atmps.231115.004
ID  - Tavkhelidze2023
ER  -
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