Illustrated is the use of isometric graph paper in the discovery of nonstandard area formulas. The use of definitions, geometric construction, record keeping, and conjectures about triangles, rhombuses, hexagons, parallelograms, isosceles trapezoids, rectangles, and trapezoids are described. (YP)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Presents a theorem and its converse to generate all of the primitive Pythagorean quadruples. Provides a BASIC program generating them. (YP)

Discusses numerical methods to compute approximate solutions of a differential equation. Provides a Pascal program for the extended Euler-Heun method. (YP)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Presents two methods for replacing a series by one converging more rapidly: regrouping the terms of a series and manipulations of power series. Describes a general algorithm for approximating the natural logarithm of any number. (YP)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Describes Fermat's last theorem and shows the proof for the case when the exponent is four. Outlines other works for the proof of the theorem, including Kummer's. Twelve references are listed. (YP)

Presents two papers commenting on previous published articles. Discusses formulas related to the determinants of sums and tests the formulas using some examples. Provides three special cases of the determinants of sums. (YP)

Describes several ways to partially levitate permanent magnets. Computes field line geometries and oscillation frequencies. Provides several diagrams illustrating the mechanism of the oscillation. (YP)

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

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)

Lists five criteria in the acceptance of mathematical theorems, such as understanding, significance, compatibility, reputation, and convincing argument. Concludes that social and language factors are involved in the process of the acceptance. (YP)