The fraction 16 over 64 has a well known, interesting property. If one incorrectly cancels the sixes, a correct answer of 1 over 4 is obtained. This is an example of a lucky fraction. In this article, the author presents several examples of lucky fractions and proves two interesting properties of these fractions. This article provides students the…

A table showing the first thirteen rows of Pascal's triangle, where the rows are, as usual numbered from 0 to 12 is presented. The entries in the table are called binomial coefficients. In this note, the authors systematically delete rows from Pascal's triangle and, by trial and error, try to find a formula that allows them to add new rows to the…

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

Proposes that a mathematical treatment of Strong Inequality Triangles (sum of any two sides is greater than the third) within the reach of high school and college students is possible. Invites further explorations of other properties of Strong Inequality Triangles. (ASK)

The graphing calculator affords the student in analysis a powerful tool to extend visualization, which was previously limited to textbook illustrations and time-consuming constructions. Provides illustrative examples used in initial classroom presentations of several topics including convergence and in student explorations of these topics. (ASK)

Discusses the effects on healing of attitude, positive thinking, and affirmations. Presents a mathematical example of hypothesis testing. Results point to the desirability of discussing such ideas with students to emphasize that the use of hypothesis testing is not simply a mechanical procedure. (ASK)

Decribes a variation on Bingo that provides a non-routine probability investigation through which students develop concepts of chance. (Author/CCM)

Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in…

Determines the theoretical probability that a regular polygon will cross a crack when dropped onto floorboards. By following two special cases, a pattern emerges that enables students to consider the general case. (ASK)

Explains a non-standard definition of an ellipse familiar to astronomers and workers in celestial mechanics but which is not usually given in undergraduate text books on mathematics. (MM)

Because one of the difficulties with the standard presentation of the Fundamental Theorem of Calculus (FTC) is that essentially all functions used to illustrate this theorem are taken from earlier material, many students never fully appreciate the essential role played by continuity in statement and proof of FTC. Introduces the sim x function that…

Outlines efforts to create mathematics-related activities for freshman/sophomore level college algebra and statistics classes at Shippensburg (Pennsylvania) University. Shares some of the ways in which these activities were created and adapted. (ASK)

Presents a brief overview of dynamical systems. Gives examples from dynamical systems and where they fit into the current curriculum. Points out that these examples are accessible to undergraduate freshmen and sophomore students, add continuity to the standard curriculum, and are worth including in classes. (MM)

Aims for students to use a combination of stochastic ideas to simulate a basketball tournament. Uses the TI-83 calculator in the activity to simulate the binomial distribution. (KHR)

Presents a problem that has been well received by students in undergraduate mathematical statistics courses. The problem is presented as a game in which students are asked to choose between two alternatives, as if they were betting. (ASK)