This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue the authors focus, on Geometry in the Measurement and Geometry strand with strong links for an integrated focus on the Statistics and Probability strand. The small unit of work on the sorting and…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

This yearbook is a reference source of direct applications of mathematics for use in grades 7-12. Topics are listed alphabetically in each of four sections: arithmetic, algebra, geometry, and trigonometry. An explanation is given as to the plan of the book, making the location of desired material easier, and an index is included. In many cases the…

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Shows that the ratio of the area of the quadrilateral formed by joining the kth points to the area of the original quadrilateral is constant whether it is convex or concave quadrilateral. Presents many geoboard or dot paper diagrams and geometrical expresssions. (YP)