The celebrated Basel Problem, that of finding the infinite sum 1 + 1/ 4 + 1/9 + 1/16 + ..., was open for 91 years. In 1735 Euler showed that the sum is pi[superscript 2]/6. Dozens of other solutions have been found. We give one that is short and elementary.

This paper is a whimsical survey of the various explanations which might account for the biblical passage in I Kings 7:23 that describes a round object--a bronze basin called Solomon's Sea--as having diameter ten cubits and circumference thirty cubits. Can the biblical pi be any number other than 3? We offer seven different perspectives on this…

The activities suggested in this article are intended for use with lower secondary school students. The "Australian Curriculum: Mathematics" states that students in lower secondary school should "investigate the relationship between features of circles such as circumference, area, radius and diameter" and "use formulas to solve problems involving…

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

The purpose of this study is to assess students' conceptual learning of electricity and magnetism and examine how these conceptions, beliefs about physics, and quantitative problem-solving skills would change after peer instruction (PI). The Conceptual Survey of Electricity and Magnetism (CSEM), Colorado Learning Attitudes about Science Survey…

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…

The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to…

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 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…

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

This document contains the fourth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Kun and Ros: (1)…

The third volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains full research report papers. Papers include: (1) Students' Use of ICT Tools: Choices and Reasons (Anne Berit Fuglestad); (2) Interaction of Modalities in Cabri: A Case Study (Fulvia Furinghetti, Francesca Morselli, and…

One schools' experiences with mathematics contests are described, with American Pi, the Great Calculator Contest, and the Forest View Math Olympics in problem solving each detailed. (MNS)

A computer simulation of the Buffon Needle Problem for estimating the value of pi is discussed. (MP)