Presents theorems about lines and lattice points, and relates these to combinatorial analysis. (RS)

A system of area measurement developed for the isometric geoboard is used to justify some relationships that are often proved using square units of area. (Author/MK)

The effects of nonexamples on the acquisition of the geometrical concept of semiregular polyhedra were examined. Results favored the treatments containing both examples and nonexamples. (TG).

Examples are given of computer activities in analytic geometry. (MK)

Introduces a special triangle for which many different problems can be posed on the basis of one unusual property. Presents three problems and considers different approaches for the first problem. Explores other mathematical problems using the "What if not?" strategy that can be used as classroom activities. (KHR)

This textbook is a course in Euclidian geometry conic sections. It was translated by the original Latin, and was revised, corrected and enlarged.

An alternate geometric interpretation of the correlation coefficient to that given in most statistics texts for psychology and education is presented. This interpretation is considered to be more consistent with the statistical model for the data, and richer in geometric meaning. (Author)

Describes the development of numbers, discussing natural and rational numbers; geometry (inscribing numbers on the number line); smoothness of motion reflected in the geometrical line; square roots; and irrational numbers. Concludes that whatever the ultimate identity of irrational numbers, what is known about them is less important than what is…

A general cubic equation ax[cubed] + bx[squared] + cx + d = 0 where a , b , c , d [is a member of R], a [not equal to] 0 has three roots with two possibilities--either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…

Many educators believe that solid modeling software has made teaching two- and three-dimensional visualization skills obsolete. They claim that the visual tools built into the solid modeling software serve as a replacement for the CAD operator's personal visualization skills. They also claim that because solid modeling software can produce…

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)

The investigation of how a circle and square lying in the same plane could intersect each other is an excellent example of geometric problem-solving. This paper explores three facets of the investigation: (1) finding out how many points of intersection are possible, (2) classifying the different ways of intersection, and (3) determining which ways…