Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

By converting functional equations to cylindrical coordinates, plotting points on cardboard, and connecting these points with thread, one can make three-dimensional string figures illustrating the behavior of functions for which the derivative is not always defined. (SD)

This paper discusses several applications of combinational mathematics to social situations and problems in the social sciences. (SD)

Sophisticated simulations using computer graphics can lead to students deducing virtually all conditions of the Central Limit Theorem. Eight graphs illustrate the discussion. (MNS)

How tedious algebraic manipulations for simplifying general quadratic equations can be supplemented with simple geometric procedures is discussed. These procedures help students determine the type of conic and its axes and allow a graph to be sketched quickly. (MNS)

Methods for getting a computer-linked plotter to do a total plot of a relation are discussed. (DT)

By changing the Euclidean metric definition, a new geometry is developed. Properties of figures are analyzed and theorems are proven in this new system. (DT)

A diagrammatic approach to invariants of knots is the focus. Connections with graph theory, physics, and other topics are included, along with an explanation of how proofs of some old conjectures about alternating knots emerge from this work. (MNS)

Graphs of exotic functions which can be defined using algebraic operations are discussed. (SD)

The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)

A transformation technique for graphing is described. (DT)

Presents a device for sketching the graph of the composite and inverse of single variable real-valued functions. Discusses some didactic methods of paths. (YP)

If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, [mu], of the population. This remarkable fact, known as the law of large numbers, holds true if samples are drawn from a population of discrete or continuous…

In this article, the author considers a student exercise that involves determining the exact and numerical solutions of a particular differential equation. He shows how a typical student solution is at variance with a numerical solution, suggesting that the numerical solution is incorrect. However, further investigation shows that this numerical…