Applied and Computational Mathematics
Volume 9, Issue 3, June 2020, Pages: 102-107
Received: May 14, 2020;
Accepted: Jun. 2, 2020;
Published: Jun. 17, 2020
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Nenad Stojanovic, Department of Mathematics, Faculty of Agriculture, University of Banja Luka, Banja, Luka, Bosnia and Herzegovina
A simple polygon that either has equal all sides or all interior angles is called a semi-regular nonagon. In terms of this definition, we can distinguish between two types of semi-regular polygons: equilateral polygons (that have equal all sides and different interior angles) and equiangular polygons (that have equal interior angles and different sides). Unlike regular polygons, one characteristic element is not enough to analyze the metric properties of semi-regular polygons, and an additional one is needed. To select this additional characteristic element, note that the following regular triangles can be inscribed to a semi-regular equilateral nonagon by joining vertices: ∆A1 A4A7, △ A2 A5 A8, △A3 A6 A9. Now have a look at triangle △A1 A4A7. Let us use the mark φ=∡(a,b1) to mark the angle between side a of the semi-regular nonagon and side b1 of the inscribed regular triangle. In interpreting the metric properties of a semi-regular equilateral nonagon, in addition to its side, we also use the angle that such side creates with the side of one of the three regular triangles that can be inscribed to such semi-regular nonagon. We consider the way in which convexity, possibility of construction, surface area, and other properties depend on a side of the semi-regular nonagon and angle φ=∡(a,b1).
Some Metric Properties of Semi-Regular Equilateral Nonagons, Applied and Computational Mathematics.
Vol. 9, No. 3,
2020, pp. 102-107.
Copyright © 2020 Authors retain the copyright of this article.
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D. G. Ball, The constructability of regular and equilateral poligons on square pinboard, Math.Gaz, V57, 1973, pp. 119—122.
A. A. Egorov, Rešetki i pravilnie mnogougolniki, Kvant N0 12, 1974, pp. 26-33.
M. Audin, Geometry, Springer, Heidelberg, 2002.
M. Polonio, D. Crnokvić, T. B. Kirigan, Z. Franušić, R. Sušanj, Euklidski prostori, PMF, Zagreb, 2008, pp. 51-57.
Kirilov, O pravilnih mnogougolnikah, funkciji Eulera i ćisla Ferma, Kvant, N0 6, 1994.
M. Panov, A. Spivak, Vpisanie poligoni, Kvant, N0 1, 1999.
M. Radojčić, Elementarna Geometrija, Naučna knjiga, Beograd, 1961.
N. Stojanović, Some metric properties of general semi-regular polygons, Global Journal of Advanced Research on Classical and Modern Geometries, Vol. 1, Issue 2, 2012, pp. 39-56.
N. Stojanović, Inscribed circle of general semi-regular polygon and some of its features, International Journal of Geometry, Vol. 2., 2013, N0. 1, pp. 5-22.
N. Stojanović, V. Govedarica, Jedan pristup analizi konveksnosti i računanju površine jednakostranih polupravillnih poligona, II MKRS, Zbornik radova, Trebinje, 2013, pp. 87-105.
N. Stojanović, Neka metrička svojstva polupravilnih poligona, Filozofski fakultet Pale, 2015, disertacija
N. Stojanović, V. Govedarica, Diofantove jednačine i parketiranje ravni polupravilnim poligonima jedne vrste, Fourth mathematical conference of the Republic of Srpska, Proceedings, Volume I, Trebinje, 2015, pp. 183-194.
N. Stojanović, V. Govedarica, Diofantove jednačine i parketiranje ravni polupravilnim poligonima dvije vrste, Sixth mathematical conference of the Republic of Srpska, Proceedings, Pale, 2017, pp. 266-280
V. V. Vavilov, V. A. Ustinov, Okružnost na rešetkah, Kvant, N0 6, 2007.
V. V. Vavilov, V. A. Ustinov, Mnogougolniki na rešetkah, Izdavateljstvo, MCIMO, Moskva, (2006.)