Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)

Investigated was the mathematical content of 15 college-level physical-geology textbooks published in the period 1980-90. A list of textbooks is provided. Methods, comparisons with other fields of science, and the treatment of specific geological concepts are discussed. (CW)

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Provides a BASIC program to compute the number of shuffles required for packs containing even numbers of cards up to 100. Lists 4 further questions on the shuffling program. (YP)

Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

Introduces four activities on forming rectangles according to specific directions. Critical reading, experimentation, logical reasoning, and validation of given directions are necessary for accuracy. Provides objectives, directions, extensions, answers, and a worksheet for each activity. (YP)

Discussed is a high school mathematics curriculum for students pursuing majors in collegiate business programs. Proposed are different emphases in the curriculum by different career fields such as audit manager, marketing manager, and production manager. (YP)

A police officer presented a question about a formula on speeding. This application was a good real-world example of radicals to present in an algebra class. How it was used is presented. (MNS)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

Presented are mathematical games in six categories of mathematical objectives: learn the language of mathematics; use mathematical notation; know facts; develop skills; understand concepts; and devise strategies. Numbers of players, rules, and diagrams are provided for each problem. (YP)

Discussed are three examples of computer graphics including biomorphs, Truchet tilings, and fractal popcorn. The graphics are shown and the basic algorithm using multiple iteration of a particular function or mathematical operation is described. An illustration of a snail shell created by computer graphics is presented. (YP)

Described is a mathematics and science unit on metric measuring for third-, fourth-, and fifth-grade students. The objective of the unit is to expose students to new situations so that they can transfer learning from the classroom to real-life experiences. Eight activities are described with figures. (YP)

Outlines a possible framework for allowing teachers to explore how children learn mathematics. A mathematical modelling process and three domains, including content, process and pragmatic domain, are described. Twelve strategies for encouraging children to translate between the domains are suggested. (YP)

Suggests computer graphing as a topic for computer programing. Reviews Apple II computer graphics information and gives suggestions for writing the programs. Presents equations to help place information onto the screen with proper coordinates. (MVL)