Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

A simple and practical application of mathematics is for fairly resolving the dispute of division of items for which two parties have equal claim. Basic properties of fair division are explained, which would enable students to learn concepts on optimization without introducing calculus.

Tessellations in the Euclidean plane and regular polygons that tessellate the sphere are reviewed. The regular polygons that can possibly tesellate the sphere are spherical triangles, squares and pentagons.

Some of the graphing capabilities of The Geometer's Sketchpad (GSP) in the "Technology Tips" are introduced. The new graphing features of GSP allow teachers to implement the software not only in geometry classrooms but also into their algebra, precalculus and calculus classes.

The research team of the Purdue University in the United States developed an algorithm that considers several different factors, in addition to cost, to help catalog distribution centers process their returns more efficiently. A case study to teach the students important concepts involved in developing a solution to the returns disposition problem…

An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…

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.

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

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…

The importance of visual representation, usually a geometric figure presented in words and in mathematical symbols that is frequently found on high-stakes standardized tests is evaluated. The study shows that mathematics teachers can help prepare students to solve mathematical problems containing a figure not drawn to scale by looking for and…

An interdisciplinary activity in which students can see how a famous author, Leo Tolstoy, metaphorically applied the integration steps from calculus to illustrate his ideas about how history should be studied is described. The activity provides a startling and energizing conclusion to a unit on applications of integration and provokes students'…

Some inexpensive or free ways that enable to capture and use images in work are mentioned. The first tip demonstrates the methods of using some of the built-in capabilities of the Macintosh and Windows-based PC operating systems, and the second tip describes methods to capture and create images using SnagIt.

Circumscribable quadrilateral is the one that contains a circle tangent to each of its side and it is assumed to be convex. The way teachers could use their own mathematical curiosity to engender the same in students, thereby showing a simple but relentless habit of questioning could lead is illustrated.

Implications and suggestions for using combinatorial mathematics in the classroom through a survey and synthesis of numerous research studies are presented. The implications revolve around five major themes that emerge from analysis of these studies.

A few problems to dispel the notion that mathematics today admits no unsolved problem are presented. The vast area of the unknown and challenges that befit a twenty-first-century attack are discussed.