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.

This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…

"Cognitive Tutor[R] Algebra I," a full year course, delivers instruction in single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The…

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…

This activity book was designed especially for the classroom teacher who is constantly on the lookout for unique and interesting ways to challenge the students' learning capacity in the area of elementary mathematics. The material presented here places a strong emphasis on defining the particular skills to be covered in each activity. All the…

The SCOPE Mathematics Achievement Test booklet for grade 5 presents 11 mathematical concepts with instructions for students to take the test with little or no teacher direction. Testing items include: writing number words; reading and writing numerals in sequence from 0.001 to 100,000; adding and subtracting whole numbers; multiplying up to four…