In this paper, using the Lambert series and other known results, the authors consider the computation of a class of series involving the powers of generalized Fibonacci and Lucas numbers, and obtain their approximate values.

A study is conducted to prove Kaprekar's conjecture with the help of mathematical concepts such as iteration, fixed points, limit cycles, equivalence cases and basic number theory. The experimental approaches, the different ways in which they reduced the problem to a simpler form and the use of tables and graphs to visualize the problem are…

Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…

Recent work has investigated children's developing understanding of the anatomical locus of identity. In two studies, we extend this work by exploring the role of the mind as opposed to the brain in children's conceptualization of identity. In Experiment 1, an analysis of natural language indicated that adults use the term mind more frequently…

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

How do people think about social status? We investigated the nature of social status and number representations using a semantic distance latency test. In Study 1, 21 college students compared words connoting different social status as well as numbers, which served as a control task. Participants were faster at comparing occupations and numbers…

Seven studies explored the empirical basis for claims that infants represent cardinal values of small sets of objects. Many studies investigating numerical ability did not properly control for continuous stimulus properties such as surface area, volume, contour length, or dimensions that correlate with these properties. Experiment 1 extended the…

The modular ring Z[subscript 6] defines integers via ( 6r[subscript i] + ( i - 3)) where i is the class and r[subscript i] the row when tabulated in an array. Since only Classes 2[subscipt 6] and 4[subscript 6] contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the…

The note considers M-bonacci numbers, which are a generalization of Fibonacci numbers. Two new summation formulas for M-bonacci numbers are given. The formulas are generalizations of the two summation formulas for Fibonacci numbers. (Contains 2 tables.)

Beautiful connections are established between seemingly unrelated mathematical territories, Fibonacci-Lucas numbers and hyperbolic trigonometric functions.

In 12 audio taped sessions, three kindergarten children engaged algebra in a teaching for understanding, thematic project. Toni, Asa, and Cornel had one-on-one lessons dealing with simple natural numbers, patterns, and relationships. Along the way, each child studied one of Toni Morrison's Who's got game books to explore repetition patterns in…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

This paper summarizes difficulties that chemistry students at all levels commonly exhibit when translating, manipulating, and interpreting mathematical expressions that contain logarithms, and offers approaches that the authors have found useful to help students overcome such difficulties. The online supplement provides problem sets created by the…

Population trends--birth and death rates, immigration patterns, sex ratios, and life expectancies--are one of the most important issues facing the international community. These trends' relationship to the world economy, the environment, and developing countries' ability to meet the needs of growing populations is a topic appropriate for the…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…