Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes properties of Fibonacci numbers, including the law of recurrence and relationship with the Golden Ratio. Discussed are some applications of the numbers to sewage of towns on a river bank, resistances in electric circuits, and leafy stems in botany. Lists four references. (YP)

Describes a number sequence made by counting the occurrence of each digit from 9 to 0, catenating this count with the digit, and joining these numeric strings to form a new term. Presents a computer-aided proof and an analytic proof of the sequence; compares these two methods of proof. (YP)

Presents examples of 3-by-3 and 4-by-4 magic squares. Proves that the numbers 1 to 10 can not be fitted to the intersections of a pentagram and that the sum of the 4 numbers on each line is always 22. (YP)

A square-dance number is defined as an even number which has the property that the set which consisted of the numbers one through the even number can be partitioned into pairs so that the sum of each pair is a square. Theorems for identifying square-dance numbers are discussed. (YP)

Shows numeral systems using base-10 positional systems currently in use in other countries. Describes two of the systems, Arab and Nepalese, and one, Chinese, that operates on a different principle. Provides references for getting more information about diverse numeral systems. (YP)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Urges that the search for origins of European exploration extend to Africa and East Asia and their international trade. Cites contributions of India and the Arabs, Chinese, and Malaysians. Emphasizes the importance of mathematics, navigation, and sailing technology. Argues that without these contributions the European voyages would not have been…

This article discusses the classroom use of discovery of number pattern. Provided are examples of a table of squares, multiplications of numbers, and algebraic expressions. (YP)

This seventh of 10 blocks of student and teacher materials for a secondary/postsecondary level course in electronic principles comprises one of a number of military-developed curriculum packages selected for adaptation to vocational instruction and curriculum development in a civilian setting. Prerequisites are the previous blocks. This block on…