Several results are explored which stem from the theorem stating that the line joining the midpoints of two sides of a triangle is parallel to and one-half of the third side. (DT)

Six different methods for bisecting a line segment are illustrated and explained. (DT)

Explains that the geometrical interpretation of general relativity provides the formalism with intuitive imagery and an interpretation often presupposes a substantival space. Special relativity can also be interpreted substantivally, which is the key to laying out an internally coherent substantivalist line running from Newtonian mechanics to…

Describes how the book "Sir Cumference and the First Round Table: A Math Adventure" was used as the basis for a series of lessons involving shapes and measurement. (Author)

Describes how modifying familiar classroom formats in a college geometry class helped encourage student problem solving. Demonstrates these modified formats in the context of problems students explored, which resemble the problem-solving settings of mathematicians. (KHR)

Presents a geometric discovery involving the use of a trapezoid as a base for a pyramid. Includes reproducible student worksheet to be used as a group-discovery exercise. (MKR)

Gives a student-accessible proof that, in any convex polyhedron, the number of vertices plus the number of faces is always two more than the number of edges. (MKR)

Recorded are some biographical data about the late professor Freudenthal along with some indications about his mathematical work. In an appendix, a tiny part of his mathematical work which can be explained in a fairly direct manner is discussed. (Author)

Interprets the philosophical concept of warrant in a mathematics education context and applies it to two central questions: (1) in what sense does mathematical proof warrant?; and (2) can there be warrants for mathematical knowledge other then deductive proofs? (Contains 36 references.) (Author/ASK)

Discusses problems similar to the Pythagorean Theorem as they were presented in historical mathematical texts from China and Babylon dating back to well before the time of Pythagoras. (ASK)

Presents situations from geometry classrooms resulting from observations of five geometry teachers and their classes. Concludes that some teachers are influenced by their beliefs, professional development experiences, and views about their own teaching. Contains 11 references. (ASK)

Presents student methods for finding out the number of different squares on a chessboard. Includes extensions of the activity. (MKR)

Gives examples of new mathematics theorems and proofs shown to the author by his students. Reflects on the notion of proof and discusses issues of multiculturalism in mathematics and descriptions of mathematics. (MKR)

Shows how geometric truths can be reinforced by simple exercises with lines and dots. (MKR)

The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)