Divisibility tests for digits other than 7 are well known and rely on the base 10 representation of numbers. For example, a natural number is divisible by 4 if the last 2 digits are divisible by 4 because 4 divides 10[sup k] for all k equal to or greater than 2. Divisibility tests for 7, while not nearly as well known, do exist and are also…

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…

A proposal is made for a careful study of the various units of measurement now in use throughout the world, combined with recall of benefits of the number system, in order to develop a new system. Suggested changes are illustrated. (MNS)

Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…

Different representations of rational numbers are considered and students are lead through activities that explore patterns in base ten and other bases. With this students are encouraged to solve problems and investigate situations designed to foster flexible thinking about rational numbers.

The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…

Numbers can be represented in a variety of ways--through pictures, diagrams, symbols. Each representation highlights different features of the number and the number system. This study aims to explore pupil understanding of number both within and across representations. A computer environment (suite of programmes) was created within which…

An imaginary journey to Planet Seven is used to introduce the concept of number systems not based on ten. Activities include making a base 7 chart, performing base 7 addition and subtraction, designing Planet Seven currency, and developing other base systems for other planets. (MT)

In a course on proofs, a number of problems deal with identities for Fibonacci numbers. Some general strategies with examples are used to help discover, prove, and generalize these identities.

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)

The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

The historical development of the integers, the rationals, the reals, and the complex numbers is traced. (MK)

An argument is made against the use of the metric system as the sole system of measurement since computers use a hexadecimal system. (MP)