English Russian
Известия
Izvestiya of Altai State
University Journal
The News of Altai State University

 Архив журнала «Известия АлтГУ», начиная с 2017 г., размещен на новой версии сайта http://izvestiya.asu.ru
 Актуальная информация о журнале размещена на новой версии сайта http://izvestiya.asu.ru

Print ISSN 1561-9443
On-line ISSN 1561-9451
Issues list
Table of Contents
Mathematics and mechanics
Management, computer engineering and informatics
Physical science
About the Journal
Editorial board and Editorial advisory board
Regulations on reviewing research papers
Rules of the articles representation
Publication Ethics of the journal «Izvestiya of Altai State University»
 
1-2(81)2014
  MATHEMATICS AND MECHANICS

Previous | Next

M.A. Cheshkova

A Cylindroid with Circular Helixes as Directing Curves

A ruled surface is called a Catalan surface if its rectilinear generators are parallel to a certain surface. A cylindroid is the Catalan surface formed by a straight-line movement along two directing curves with a rectilinear generator being parallel to a certain surface. In the paper we study cylindroids with circular helixes as directing curves. There are four cases: 1) the two helixes are rightrotary and they have the same screw pitch, 2) the two helixes are right-rotary and they have different screw pitches, 3) one helix is right-rotary, the second helix is left-rotary and they have the same screw pitch, 4) one helix is right-rotary, the second helix is left-rotary and they have different screw pitches. Total and the mean curvatures of the considered surfaces are calculated. The mean curvature equals to zero in the first case only. The only surface is the minimal surface. A helicoid is the only minimal ruled surface. We construct these surfaces with a help of mathematical software package.

DOI 10.14258/izvasu(2014)1.2-11

Key words: cylindroid, helix, total curvature, mean curvature

Full text at PDF, 571Kb. Language: Russian.

CHESHKOVA M.A.
Altai State University (Barnaul, Russia)
E-mail: cma@math.asu.ru

 

Print Edition of "Izvestiya of Altai State University" © 1996-2017 Altai State University.
All rights reserved. Any of parts of a journal or edition as a whole cannot be reprinted without the written sanction of the authors or publisher. On purchase of a journal to address to ASU publishing house:
Altai State University. 656049, 66 Dimitrova street, Barnaul, Russia. Telephone + 7 (3852) 366351.