In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)

Trends in International Mathematics and Science Study raised the concern that the United States (US) mathematics teachers place less emphasis on topics and teach a variety of content strands (Goldsmith, Mark & Kantrov, 2000; Kerachsky, 2008). The overall pattern in the US mathematics classrooms today is that primary and upper elementary…

The Chinese tangram puzzle was known as far back as 1813. It has remained popular ever since. It consists of seven simple polygonal pieces of card which can be assembled in the form of a square. The reader is presented with some popular shape such as the man or cat above, and then asked to construct this using the tangram pieces. There are whole…

In this article quadrilaterals with concurrent maltitudes are characterized. A generalization of the maltitudes is given, and a larger family of quadrilaterals for which an analogous property of concurrency holds is determined and studied.

A simple way to represent hemihedral faces and to illustrate the relationship between the resulting left-handed and right-handed hemihedra is presented. The illustrations highlight that the chirality corresponds to the absence of reflective symmetry but not necessarily to the absence of a C2 axis of symmetry.

The properties of a dendrimer with hydrophobic and hydrophilic substituents on an orthogonal plane is synthesized and studied. The resulting polymer contains one of the substituents in its concave interior and the other at the convex surface and the design promotes micelle-like behavior in polar solvent and inverted micelle arrangement in…

The ancient Greek mathematicians sought to construct, by use of straight edge and compass only, all regular polygons. They had no difficulty with regular polygons having 3, 4, 5 and 6 sides, but the 7-sided heptagon eluded all their attempts. In this article, the authors discuss some cosine relations and the regular heptagon. (Contains 1 figure.)

In this paper the didactically-methodological procedure named the MTE-model of mathematics teaching (Motivation test-Teaching-Examination test) is suggested and recommended when the teacher has subsequent lessons. This model is presented in detail through the processing of a nonstandard theme--the theme of decomposition of planes. Its efficiency…

MATERIALS ARE INTENDED FOR A UNIFIED AND ACCELERATED PLANE AND SOLID GEOMETRY COURSE AND FOR EASY MODIFICATION AND ADAPTATION BY EXPERIENCED OR INEXPERIENCED TEACHER. TEXTBOOKS TO WHICH THE GUIDE HAS BEEN KEYED ARE LISTED. UNITS ARE GIVEN FOR BOTH SEMESTERS WITH TIME ALLOTMENTS RECOMMENDED. EACH UNIT IS SUBDIVIDED INTO TOPICS AND OBJECTIVES,…

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

An exploration of nonconvex, crossed, and degenerate polygons (NCCDPs) are described with the help of examples with pedagogical tips and recommendations that are found useful when teaching the mathematical process of extending geometric patterns to NCCDPs. The study concludes that investigating such extensions with interactive geometry software…

Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)