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.

The five mathematics problems to be solved by high school students participating in the Fifth U.S.A. Mathematical Olympiad are given. (DT)

A problem is posed concerning the area of certain parts of a plane geometric figure. The problem was used in a student contest with 71 of 270 mathletes answering correctly. An outline of the general proof is given. (LS)

This monthly column contains teaching suggestions on: using codes to convey information, flow proofs in geometry, and volleyball and probability. (MP)

The author has selected a number of episodes that illustrate some of the successes and failures of humanity's attempt to find the area of the circle and presents them as problem studies. (MN)

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

Answers to a list of twenty geometry-related questions are hidden in a matrix of letters. The answers can be read in eight different directions: vertically, horizontally, on both diagonals, forward, and backward. (MN)

Five basic skill areas needing more attention in standard high school geometry are discussed. Levels of student mental development in geometry and a need for less emphasis on formal proofs are reviewed. (MP)

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)

Presents 14 distinct methods to determine the sine of the angle formed by the line segments joining one vertex of a square to the midpoints of the nonadjacent sides. Nine methods were developed by mathematics club participants preparing for mathematics competitions and the remaining five by faculty members. (MDH)

Provided are the activity sheets for students and the teaching guide for this middle school geometry activity. Materials, prerequisites, objectives, and procedures are listed. Extension activities are suggested. An answer key is included. (CW)

Presents two ancient problems, trisecting any angle and dividing a circle into any number of equal parts. Illustrates how to use these problems to prompt students to think broadly and creatively about problems instead of letting the apparent boundaries of the problem limit their thoughts. Combines three-dimensional solutions to the problems to…

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)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)