A variety of approaches to the concept of oxidation and reduction appear in organic textbooks. The method proposed here is different than most published approaches. The oxidation state is calculated by totaling the number of heterogeneous atoms, [pi]-bonds, and rings. A comparison of the oxidation states of reactant and product determine what type…

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)

Presented with appropriate formulas and illustrations are five lessons suitable for college mathematics undergraduate students, including Pi and the limit of (sin alpha)/alpha, the structure of orthogonal transformations, a simple proof of Zorn's Lemma, the converse of Liouville's Theorem, and visualizing the p-adic integers. (JJK)

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

Three of the modules deal with applications of calculus to other mathematics. These are: 240-Pi is Irrational; 241-The Wallis Approximation of Pi; and 242-Buffon's Needle Experiment. The first of these units focuses on a proof of the irrational nature of pi, and provides exercises and answers. The second module of this group reviews the history of…

Examines the internal consistency and temporal stability of informant ratings from the revised NEO Personality Inventory (NEO PI-R) (P. Costa and R. McRae, 1992) and the Interpersonal Adjective Scale (IAS) (J. Wiggins, 1995) through ratings by 109 undergraduates of well-known adult targets. The estimates of internal consistency and temporal…

This is a not-so-serious discussion of accidental patterns involving chance patterns between mathematics and natural laws and accidental patterns involving the numbers "pi" and "e." (Author/SA)

Computing pi efficiently has been of great interest to mathematicians for centuries. This article presents an algorithm to solve this problem through skillful computer use. (PK)

This book, written primarily for college students who feel uncomfortable with mathematics, attempts to provide its readers with new ways of thinking about mathematics, reading mathematics, studying mathematics, talking the language of mathematics and appreciating the power of using mathematics. Chapter 1 deals directly with the problem of math…

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

The Monte Carlo procedure of generating random points that lie within the unit square is used to approximate pi, as the ratio of points within the first quadrant of the unit circle to the total number of randomly generated points. A BASIC computer program for this method is included. (JJK)

The evolution of Archimedes' method is traced from its geometrical beginning as a means to approximate pi to its modern version as an analytical technique for evaluating inverse circular and hyperbolic functions. It is felt the web of old and new algorithms provides considerable instructional material, and ideas are offered. (MP)

The National Science Foundation (NSF) supported more than 600 inservice teacher training programs between 1984 and 1989 under its Teacher Enhancement Program (TEP). Two studies were undertaken of TEP: the first was a survey of the 600 Principal Investigators (PIs) who had operated inservice teacher enhancement projects and the second, a survey of…

This study documents the effects of participation in the Teacher Enhancement Program (TEP) of the National Science Foundation (NSF). The NSF awarded more than 600 grants to scientists, mathematicians, and educators to develop and operate inservice teacher training programs between 1984 and 1989. The present study focuses specifically upon the…

This paper offers a brief description of the Taiwanese elementary school system. It also outlines the current teacher training system, emphasizing the differences between the old "Normal Education Art" and the new "Teacher Education Art". One section describes the three major reforms that Taiwan's mathematics curriculum has undergone in the last…