Describes the Circle Scribe Disk Compass and explains its use in helping children to explore patterns and geometry. Topics include Fibonnacci's spiral and regular polygons. (MM)

The ability to display an accurate image is commonly assumed to be a benefit of dynamic geometry software--it seems reasonable to conclude that the task of noticing and interpreting relationships between objects is easier if figures are drawn to scale. However, results of a study involving preconstructed, web-based, dynamic, geometry sketches in…

Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.

Two technology-oriented activities are used successfully with entry-level geometry students during their study of symmetry. Reflection symmetry gives students opportunities to deepen their understanding of fundamental mathematical concepts like slope and symmetry, in a flexible and self-paced way.

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.

American university offers a course in finite mathematics whose focus is difference equation with emphasis on real world applications. The conclusion states that students learned to look for growth and decay patterns in raw data, to recognize both arithmetic and geometric growth, and to model both scenarios with graphs and difference equations.

A dynamic program for geometry called Cabri Geometry II is used to examine properties of figures like triangles and make connections with other mathematical ideas like ellipse. The technology tip includes directions for creating such a problem with technology and suggestions for exploring it.

Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…

There are four Euclidean centres of a triangle--the circumcentre, the centroid, the incentre and the orthocentre. In this article, the authors prove the following: if the centre is the incentre (resp. orthocentre) then there exists a triangle with given distances of its vertices from its incentre (resp. orthocentre). They also consider uniqueness…

Geometric constructions have previously been shown that can be interpreted as rays of light trapped either in polygons or in conics, by successive reflections. The same question, trapping light in closed Fermat curves, is addressed here. Numerical methods are used to study the behaviour of the reflection points of a triangle when the degree of the…

Mathematical historians place Heron in the first century. Right-angled triangles with integer sides and area had been determined before Heron, but he discovered such a "non" right-angled triangle, viz 13, 14, 15; 84. In view of this, triangles with integer sides and area are named "Heron triangles." The Indian mathematician Brahmagupta, born in…

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

The current mantra in education is "technology, technology, technology." Many teachers and prospective teachers become frustrated with their lack of knowledge regarding the "appropriate" use of technology in the classroom. Prospective teachers need training in their education to understand how technology can be used "appropriately" in the…

There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

This article offers an introductory activity for the limit concept with a geometrical and historical foundation. A connection among Geometry, Measurement and Calculus is highlighted with the help of technology. The geometrical drawing, measurement and graphing capabilities of both TI-89 and Geometer's Sketchpad make it possible for students to…