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 interesting construction of a conic from an ellipse given by Manuel Santos-Trigo is evaluated. The validity of the conclusion that the locus is a conic section, the nature of which is determined in a simple way by the location of the variable point R relative to its center point O and the major vertices of the ellipse are proved.

At first geometry was a practical subject to be used in the physical world. Then it took on another role as a system of thought and it became geometry for the mind. This issue's "scrapbook" consists mainly of interesting anecdotes related to geometry.

This study examined the knowledge and strategies that young children used for comparing sizes of geometric figures. Sixty-nine children from the ages 3 to 6 years were asked to compare sizes of geometric figures and their placement and adjustment strategies were observed. The children were also presented with strategies for comparing sizes and…

When young children copy a vertical line that protrudes from the midpoint of a pre-drawn oblique baseline, they tend to perpendicularise this line. We measured this bias for standard figures and for symmetrical angular figures. The 5- and 6-year-old participants produced the expected bias for the standard figures. However, these same children…

Students' difficulty with reasoning and justification in the context of proofs in geometry has been well documented. Studies reveal that many of the ideas that students are asked to prove are known to be true, and therefore, the process of such proof is likely to remain meaningless and purposeless. The implication of this claim is that students…

The location of the number "c" arising from Cauchy's Average Value Theorem is described when the size of the interval is small. This article discusses various generalizations of theorem 1, to the context of Cauchy?s Average Value Theorem--but without appealing to theorem 1. Obviously, hypotheses involving the functions "f" and "g" will be…

Nature is full of different crystals and many of them have shapes of regular geometric objects. Those in which the fractal structure of a geometric object can be recognized are especially unusual. In this paper a generalization of one of these shapes is described: a formation, based on an n-dimensional simplex. The construction of an n-dimensional…

A study is conducted regarding the change in teaching process in the geometry of transformations, teaching by small steps rather than by a complicated method. In the process of making mathematics teaching better, many challenges are faced, and several risks are taken to solve the questions asked by the students.

This article contains investigative activities to assist students in constructing formulas out of an understanding of the area of geometric shapes. Included with this article are a "Finding Areas on Square Dot Paper Activity Sheet" and a "Finding Areas on Triangle Dot Paper Activity Sheet." (Contains 1 table and 11 figures.)

For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates,…

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for the author, 3-D geometry is the branch of mathematics that shows…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…