Examines the roles of experimental tasks in "Elementary Geometry" (1903) by Godfrey and Siddons, which is considered one of the most important geometry textbooks in the history of geometry teaching. Roles of experimental tasks included preparations for deductive geometry and, even though it is implicit, the verification of geometrical facts.…

Discusses the new Standards' vision for teaching geometry in the middle grades, specifically geometry connections in the middle grades across the Standards. Students learn geometry within an integrated mathematics program that prepares them to solve problems in school and in their personal lives. (ASK)

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…

Defines tessellations as closed geometric shapes that completely cover a surface without gaps or overlaps. Suggests how they can be used in technology class activities. (JOW)

Discusses some questions connected with Cauchy's theorem which states that two convex closed polyhedral surfaces whose corresponding faces are congruent and whose faces adjoin each other in the same way are congruent. Describes how to construct a flexible polyhedron. (ASK)

Examines why a flexible polyhedron must be convex. Discusses the theorems of Cauchy and Euler. (ASK)

Describes empirical research into the effectiveness of using concepts and principles of physics in the teaching of geometrical proofs. Demonstrates, tentatively, that proofs from physics could be a viable addition to the mathematics curriculum. (Author/MM)

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.

We report some findings of the Longitudinal Proof Project, which investigated patterns in high-attaining students' mathematical reasoning in algebra and in geometry and development in their reasoning, by analyses of students' responses to three annual proof tests. The paper focuses on students' responses to one non-standard geometry item. It…