Fractal geometry is introduced through examples of computational exploration of coastlines, self-similar curves, random walks, and population growth. These explorations, which include the construction of algorithms and the subsequent development and application of simple computer programs, lend themselves to self-directed study and advanced…

Graphs equations in two variables using a BASIC screen-sweep program that generates solutions to equations by applying the intermediate value theorem. Provides suggestions for investigations that result in graphs of a butterfly, the Cheshire cat, the Trisectrix of Catalna, E. T. waving goodbye, a praying mantis, and others. (MDH)

Presents 12 problems for students to investigate the relationships involving properties of numbers by using BASIC language. (YP)

Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)

Focuses on the place of discrete mathematics in the grades 9-12 mathematics curriculum and discusses how the topic of recursion should be taught. Presents several examples of recursion involving LOGO, spreadsheets, sequences, Pascal's triangle, and the Tower of Hanoi to illustrate its teaching. (MDH)

Provides Terrapin LOGO programs that use graphic manipulatives--squares, logs, and units--to form the area of a rectangle as a graphical representation for any trinomial of the form: Axx + Bx + C. An important component is the connection of the procedural skill of trinomial factoring to the visualization of the accompanying rectangular displays.…

Described are materials developed to add to existing complex-number units and how they have been used in second-year algebra and precalculus classes. Discussed is software developed, objectives, and classroom materials. Two worksheets are included. A computer program is provided. (CW)

Described is a LOGO computer program that enables students to investigate the relationship between a digital number and the resistance in a variable resistor used to generate that number. Likewise, actual temperature readings and the corresponding resistance within a thermistor can be used for data gathering and subsequent analysis. (JJK)

Describes a process of mathematical investigation involving generalized Fibonacci sequences. Provides the derivation using expressions, BASIC programs, and numerical verification. (YP)

Described is a solution to the problem and a discussion of a computer estimation of the probability. A computer program written in Turbo Pascal and two sample runs are provided. Computations for a more general problem of this nature and changes in the program necessary for use with Apple Pascal are appended. (CW)

The LOGO subroutine turtle geometry and Euclidean geometry are compared with respect to their treatment of similarity and difference of plane figures. The problem and its proposed solution of introducing a FLIP operation are viewed briefly from the perspectives of mathematics, computer science, and education. (MDH)

Describes how three dimensional LOGO was used in a workshop session for secondary pupils and mathematics teachers. Provides many commands and output drawings. (YP)

A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

In polar coordinates, the intersection of the graphs of two functions, f(x) and g(x), does not always correspond to the solutions of the equation f(x) = g(x). Presented are examples to illustrate this concept, proofs demonstrating why this is true, and a computer program to simultaneously plot polar coordinate graphs. (MDH)

Described is a recursive LOGO method for dissecting polygons into congruent parts (rep tiles) similar to the original polygon, thereby producing unexpected patterns. A list of descriptions for such dissections is included along with suggestions for modifications that allow extended student explorations into tile patterns. (JJK)