The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…

Children often incorrectly reduce fractions by canceling common digits instead of common factors. There are cases, however, in which this incorrect method leads to correct results. Instances, such as 16/64 and 19/95, are well-known. In this paper, we consider such "weird fractions" and show how examples of them can be multiplied "ad infinitum" and…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Describes the experiences and conclusions of a long-range program to revitalize undergraduate instruction in mathematics utilizing state-of-the-art workstations and the computer algebra system, Maple, and includes two examples of this type of instructional improvement. Focuses on computer-intensive calculus. (MKR)

Described are several programs that enable the user to evaluate derivatives to order n of any elementary function by using the combination of automatic differentiation method and A Programming Language (APL). Programs calculating first- and higher-order derivatives are presented. Selected APL symbols are appended. (YP)

Proposes the use of conceptualization, exploration, and higher-level problem solving in differential equations courses as a replacement for some of the traditional material that can now be delegated to the computer. (MKR)

Discussed is an application of the computer software package, "Mathematica," to solve typical optimization problems from freshman calculus. An example of the use of this method is provided. (CW)

Reviewed are two computer software packages for Macintosh microcomputers including "Phase Portraits," an exploratory graphics tool for studying first-order planar systems; and "MacMath," a set of programs for exploring differential equations, linear algebra, and other mathematical topics. Features, ease of use, cost, availability, and hardware…

Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)

Shows step-by-step use of spreadsheets with an example from linear programing using the Simplex method. Describes pivot choosing and partial Gauss-Jordan elimination procedures. (YP)

Presents an example using a computer to illustrate concepts graphically in an introductory course on differential equations. Discusses the algorithms of the computer program displaying the solutions to an equation and the inclination field of the equation. (YP)

Presents examples of using the computer to enhance teaching function evaluation using BASIC, Riemann sums using MAPLE computer algebra systems, and linear programing using MATLAB. (YP)