"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

Gives several proofs of the converse of the Pythagorean Theorem. (MKR)

Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

The results of investigations into finite geometries, prompted by questions raised in a course for secondary school mathematics teachers, are presented. The discussion of points, lines, and incidences led to consideration of graphs of second-degree equations in finite projective planes. (MNS)

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)

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)

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

Focuses on improving geometry teaching by: (1) identifying the meaning of "transforming spatial operations into logical ones;" (2) embodying this meaning in several exemplary experiences; and (3) commenting and reflecting on the significance of the geometrical operations underlying the experiences. (JN)

Discusses the formation of a geometry club in which members (students, teachers, staff) of a high school meet in order to discuss and demonstrate the mathematics in Euclid's Elements. (MKR)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

Describes features and uses of the Geometry Forum, a National Science Foundation funded Internet project which includes a set of electronic newsgroups for people interested in geometry. (MKR)

Provides practical applications of elementary coordinate geometry while discussing how mathematics is used to assess the security of systems. (ASK)