The present problem was derived from the knowledge that if the midpoints of the sides of any quadrilateral are connected, a parallelogram would be obtained. The author explores what would happen if similar procedures were applied to pentagons, hexagons, and other geometric forms. (RP)

Presents two equivalent forms of the Pythagorean theorem, and a form for finding the area of a right triangle. (RP)

Excerpts from the April 1950 issue of this journal, focusing on the teaching of geometry, are presented. The concern is its lack of importance in the curriculum. (MNS)

The non-Euclidean taxicab geometry is described and contrasted with Euclidean geometry, with examples teachers could use with students. (MNS)

A math teacher suggests redesigning geometric studies to emphasize career education. (Editor)

A problem concerned with a ball on a billiard table is discussed. A theorem and corollaries regarding the path of the ball are formulated and proved. (MK)

The topics of angle construction, angle trisection, and regular polygon construction with only a straightedge and compass are discussed for angles with integer measure. (MP)

A method is developed for finding the equations of two circles that intersect at points with integral coordinates. Such equations are useful for the introducing systems of quadratic equations. (MP)

Two units are developed that provide the student with experience in constructing auxilary lines that are often needed in formulating geometric proofs. (MP)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Detailed descriptions are given of two procedures for measuring the radius of the earth, one using a rule and the other a stopwatch. (MP)