As geometry involves lot of graphics, it acts as a link between mathematical model and real-world phenomena. An effective tool like geometry software can help students to explore the ellipse.

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

Ever since the first mariners sailed off the east coast of Scotland the Bell Rock has claimed many vessels and countless lives. Also known as the Inch Cape Rocks they lie 18 km off the coast at Arbroath. Located near the mouth of the Firth of Forth and its important shipping ports these dangerous rocks cover an area some 440 m long and 90 m wide.…

In this article, the authors talk about transformation geometry being treated as little more than a set of tricks rather than as a mathematically rigorous topic. This appears to lead to pupils seeing little point in studying "reflections, rotations and translations" as other than examinable items in some future test. Following the argument…

In this article, the authors describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions. They list three major ways in which one can imagine the environment and problems being used by teachers. Among other things, they discuss how the environment could support teaching and learning, and how the…

Examines how constraint-based 3D modeling can be used as a vehicle for rethinking instructional approaches to engineering design graphics. Focuses on moving from a mode of instruction based on the crafting by students and assessment by instructors of static 2D drawings and 3D models. Suggests that the new approach is better aligned with…

Categories can be counted, rated, or ranked, but they cannot be measured. Likewise, persons or individuals can be counted, rated, or ranked, but they cannot be measured either. Nevertheless, psychology has realized early on that it can take an indirect road to measurement: What can be measured is the strength of association between categories in…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

We sometimes teach our students a method of finding all integral triples that satisfy the Pythagorean Theorem x[squared]+y[squared]=z[squared]. These are called Pythagorean triples. In this paper, we show how to solve the equation x[squared]+ky[squared]=z[squared], where again, all variables are integers.

This article describes activities that introduce basic trigonometric functions in a smooth and natural way. The only requirements are basic algebra, the Pythagorean theorem, and the concept of area.

When students take General Chemistry there are substantially fewer molecular images than they will encounter in Organic Chemistry. The molecular images Organic Chemistry students see in their textbooks are ones that use dashes and wedges to represent 2D and semi 3D views, ball and spoke, ball and wire, and structural formulas, to name just a few.…

The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

This article describes how a series of lessons might be used to allow students to discover the size of the Earth, the distance to the Moon, the size of the Moon, and the altitude of Mount Piton on the Moon. Measurement with a sextant, principles of geometry and trigonometry, and historically important scientists and mathematicians are discussed.