• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.183-197
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• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• East Asian mathematical journal
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• v.31 no.4
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• pp.483-503
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• 2015

While some studies have examined the concave and convex regular polygons respectively, very little work has been done to integrate and restructure polygon shapes. Therefore, this study aims to systematically reclassify the regular polygons on the through a comprehensive analysis of previous studies on the convex and concave regular polygons. For this study, the polygon's consistency with respect to the number of sides and angles was examined. Second, the consistency on the number of diagonals was also examined. Third, the size of the interior and exterior angels of regular polygons was investigated in order to discover the consistent properties. Fourth, the consistency concerning the area in regular polygons was inspected. Last, the consistency of the central figure number in the "k-th" regular polygons was examined. Given these examinations, this study suggests a way to create a concave regular polygon from a convex regular polygon.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.119-134
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• 2008

In this paper we study a book 'Method of Ruler and Compass' written in Russia three hundreds years ago. In this book many construction problems related with plane figures and solid figures are solved. In this study we analyze construction method of some regular polygon(square, regular pentagon, regular octagon, regular decagon) suggested in 'Method of Ruler and Compass', give mathematical proofs of these construction.

• Journal of KSNVE
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• v.6 no.5
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• pp.587-594
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• 1996

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.935-940
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• 2006

Numerical methods are developed for solving the elastica and buckling load of cantilever column with constant volume, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the horizontal deflection at free end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.

• Journal for History of Mathematics
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• v.29 no.2
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• pp.73-88
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• 2016

To introduce materials related to our traditional mathematics and to reinterpret modernly them could be a good tool to find the cultural values of them. We analyzed the degree for utilization of the history of mathematics in the middle school textbooks developed depending on the 2009 revised mathematics curriculum. Through this, we suggest the need for research on concrete and practical teaching and learning materials development utilizing the history of mathematics. We reinterpret, in modern style based on the curriculum, two subjects dealt with in 'GakDeungByeonHyeongSeupYu', the first theme of 'SanSulGwanGyeon' written by Lee Sang Hyuk. We expansively reconstruct the original samples up to regular decagon so that students might figure out the situation of all regular polygon using a kind of mathematics software GeoGebra. Also this process is constructed on the basis of the curriculum for an implementation the secondary school classes.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.527-530
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• 1997

An automated process planning system for cold forging of non-axisymmetric parts of comparatively simple shape was developed in this study. Programs for the system have been written with Visual LISP in the AutoCAD using a personal computer and are composed of four main modules such as input module, shape cognition and shape expression module, material diameter determination module and process planning module. The design rules and knowledges for th system are extracted from the plasticity theories. handbook, relevant reference and empirical knowledge of field experts. Generally, in forging, only front view is needed for expression of axisymmetric parts, but non-axisymmetric parts are needed both front view and plane. At the plane, this system cognizes the external shape of non-axisymmetric parts - number of sides of regular polygon and radius of a circle circumscribing the polygon of n sides. At the front view, the system perceives diameter of axisymmetric portions and hight of primitive geometries such as polygon, cylinder, cone, concave, convex, etc.

• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.2
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• pp.144-152
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• 2010

This paper deals with free vibrations of the tapered circular arches with constant volume, whose cross sectional shape is the solid regular polygon. Volumes of the objective arches are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear, parabolic and sinusoidal ones. Ordinary differential equations governing free vibrations of such arches are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various arch parameters such as rise ratio, section ratio, side number, volume ratio and taper type are reported in tables and figures.