Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…

In early childhood and primary (PreK-2) grades, subitizing is a critical skill that helps children meet early mathematics standards. Discover ways teachers can infuse this critical skill into their math curriculum.

Illustrates a way in which students can estimate the ratio of an area of a circle using the radius square. Discusses why the same value of pi appears in both the formulas for the circumference and the area of the circle. (YDS)

This paper considers a group of preservice teachers' construction of concept maps derived from y = x + 5 and y = [pi]x[squared] with emphasis on their conceptual understanding of function. The two statements are perceived to represent a number of different concepts with indications of compartmentalized knowledge structures that might prevent the…

This paper reports on a design experiment conducted to explore the construction of meanings by 17 year old students, emerging from their interpretations and uses of algebraic like formalism. The students worked collaboratively in groups of two or three, using MoPiX, a constructionist computational environment with which they could create concrete…

A "k"-out-of-"n" system functions as long as at least "k" of its "n" components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting…

Discusses the geometric and mathematical features of the pyramids in Cairo. Describes the relationship between the great pyramid and Pi. (ASK)

In the nineteenth century many people tried to seek a value for the most famous irrational number, [pi], by means of an experiment known as Buffon's needle, consisting of throwing randomly a needle onto a surface ruled with straight parallel lines. Here we propose to extend this experiment in order to evaluate other irrational numbers, such as…

In 1998 the National Science Foundation launched the Integrative Graduate Education and Research Traineeship (IGERT) program, a major initiative aimed at Science, Technology, Engineering, and Mathematics (STEM) graduate education. IGERT was developed to meet the challenges of educating U.S. Ph.D. scientists, engineers, and educators with…

School improvement initiatives have been the focus of recent political agendas, professional conferences, and publications. A recent educational change initiative in Indiana has been Project Lead The Way (PLTW). According to Rogers (2005) the state's technology education teachers have embraced PLTW and its infusion into the high school curriculum.…

An activity for generating approximations of pi is described. (MK)

Teaching teachers to become observers and inquirers into mathematics will help change how they teach math to students. Essential to all professional development in mathematics is the idea that making sense of mathematics is key to learning. Just as learning to read calls for bringing meaning to the printed page, learning math calls for bringing…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…

Provides information about mathematician Jamshid al-Kashi and his work on calculating mathematical values such Pi or Sin(1). (ASK)