МОЖНО ЛИ ПОСТРОИТЬ ПРАВИЛЬНЫЕ МНОГОУГОЛЬНИКИ  С НЕЧЕТНЫМИ СТОРОНАМИ С ПОМОЩЬЮ ЦИРКУЛЯ  И ЛИНЕЙКИ БЕЗ ДЕЛЕНИЙ?

Равиль Рашидович Нигматуллин

Равиль Рашидович Нигматуллин Kazan National Research Techniсal University named after A.N.Tupolev

Keywords: Regular polygons with an odd number of sides, problem of trisection of an arbitrary angle, compass with notches, ruler without divisions.

Abstract

This brief article deals with new possibilities of constructing regular polygons with the number of sides expressed by odd numbers like 3,5,7,9,... The method proposed in the article (understandable to any advanced high school student) allows to solve such a venerable problem as trisection of an angle, division of a segment into parts expressed by odd numbers, with the help of a ruler without divisions and a circular, allowing to make serifs, and an ordinary lead pencil. It turns out that an ordinary pencil with a lead thickness of half a millimeter also plays an important role in solving this problem.

Author Biography

Равиль Рашидович Нигматуллин, Kazan National Research Techniсal University named after A.N.Tupolev

Doctor of Physical and Mathematical Sciences, Professor of the Department of Radio Electronics and Control and Measuring Equipment of KNITU-KAI named after A. N. Tupolev.
Area of scientific interests - dielectric spectroscopy of heterogeneous (self-similar) systems; physics of fractals and fractional calculus and its application to describe relaxation phenomena in complex media, development of new methods for isolating weak signals from noise in open (complex systems).
ORCID: 0000-0003-2931-4428
E-mail: renigmat@gmail.com

IS IT POSSIBLE TO CONSTRUCT REGULAR POLYGONS WITH ODD SIDES USING A COMPASS AND A RULER WITHOUT DIVISIONS?

Abstract

Author Biography

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