Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

This article traces the history of the number [Pi] from 3000 BC (the construction of the Egyptian pyramids) to 2005 (the calculation of the first 200 million digits of Pi).

For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…

This article employs the Archimedean method of estimating the value of pi within an inscribed pentagon. We show how to write these approximations in terms of the golden ration.

Three major techniques are employed to calculate [pi]. Namely, (i) the perimeter of polygons inscribed or circumscribed in a circle, (ii) calculus based methods using integral representations of inverse trigonometric functions, and (iii) modular identities derived from the transformation theory of elliptic integrals. This note presents a…

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…

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)

Reprinted is "Shanks, Ferguson and pi" by T. A. A. Broadbent. It describes the historical development of the mechanical calculation of the number pi. (CT)

The history of the two numbers e and pi is traced, and the relationship of thesetwo numbers to the history and development of mathematics is indicated. (DT)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

Spatial ability has been recognized as one of the most important factors affecting the mathematical performance of students. Previous studies on spatial learning have mainly focused on developing strategies to shorten the problem-solving time of learners for very specific learning tasks. Such an approach usually has limited effects on improving…

Several problems involving "pi" and "e" can be approached by diagramming, flow charting, and computer programing. (SD)

This document contains the third volume of the proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics. Conference presentations are centered around the theme "Inclusion and Diversity". A total of 65 research reports are presented here: (1) A Teacher's Model of Students Algebraic Thinking About…

Approximating the limits of certain convergent series is discussed as a method for students to use in calculating an approximation for pi. (FL)

Provides a software program for determining PI to the 15th place after the decimal. Explores the history of determining the value of PI from Archimedes to present computer methods. Investigates Wallis's, Liebniz's, and Buffon's methods. Written for Tandy GW-BASIC (IBM compatible) with 384K. Suggestions for Apple II's are given. (MVL)