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.

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…

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

This paper describes the analysis of the National Science Foundation (NSF) Math and Science Partnership (MSP) program's January 2008 Learning Network Conference (LNC). This study focuses on the methodologies used by the MSP community to generate evidence and seeks to understand topics of interest to the 320 LNC participants. The data set for this…

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…

We provide a geometric proof of the formula for the sine of the sum of two positive angles whose measures sum to less than [pi]/2. (Contains 1 figure.)

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…

An anharmonic solution to the differential equation describing the oscillations of a simple pendulum at large angles is discussed. The solution is expressed in terms of functions not involving the Jacobi elliptic functions. In the derivation, a sinusoidal expression, including a linear and a Fourier sine series in the argument, has been applied.…

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…

Provides a summary of the findings of nearly one hundred-fifty studies dealing with self-paced instruction S(PI) mathematics programs that involved students at the secondary level with some implications for practice. (Author/RK)

The theory of action upon which high-stakes accountability policies are based calls for systemic reforms in educational systems that will emerge by pairing incentives for improvement with extensive and targeted technical assistance (TA) to build the capacity of low-performing schools and districts. To this end, a little discussed and often…

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)

The area of a constant-width band is shown to be twice the length of its middle section times its width "h." The length of the middle section is shown to be equal to the length of the inner boundary plus [pi]"h." These results are obtained using the change of variables formula for double integrals.

An analytic approximation of the solution to the differential equation describing the oscillations of a simple pendulum at large angles and with initial velocity is discussed. In the derivation, a sinusoidal approximation has been applied, and an analytic formula for the large-angle period of the simple pendulum is obtained, which also includes…