Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

A critical examination of two key aspects of Piaget's account of how small children come to understand basic number concepts. (Author/CS)

THE MORPHOLOGICAL CHARACTERISTICS OF CZECH NOMINALS, WHICH CONSIST OF NOUNS, ADJECTIVE, NUMERALS AND PRONOUNS, ARE DESCRIBED IN THIS PREPRINT. THE PAPER DISCUSSED EACH CATEGORY SEPARATELY, DIVIDING IT INTO SUBCLASSES, AND PROVIDES ILLUSTRATIONS IN CZECH. IN THE PARADIGMS, SEPARATE FORMS FOR THE VOCATIVE ARE GIVEN FOR MASCULINE AND FEMININE NOUNS…

Based on a theory of rational numbers which sees the rational numbers construct of a person as potentially built on a number of subconstructs, this study explored the view of rational numbers as operators. Significant changes in performance level and quality appeared between ages 11 and 12 and 12 and 13. (JC)

Two experiments examined the ability of preschool children to reason about the numerical relations greater than and less than. Results showed that children as young as 21/2 years of age could make number-based relational judgments and compare two number pairs on the basis of a common ordering relation. (Author/JMB)

To investigate the effect on young children's coding of spatial information, an array of boxes was varied in number, size, and arrangement and was shown to 20 toddlers. Only the number of boxes defining the left and right sides of the array influenced performance; that is, multiple boxes were associated with the use of external objects as spatial…

A multiple baseline design was used to demonstrate the effectiveness of a self-instruction training sequence across three groups of three preschool handicapped students to improve their ability to count a requested number of objects from one to ten. Eight of nine students showed improved accuracy in counting objects and generalized these gains to…

Students who discover how to count by tens starting at a number other than 10 learn about the basic structure of the decimal system in addition. (CL)

Investigates the ability of 24 children ages two, three, and four to discriminate between two small object collections on the basis of numerosity and to maintain that discrimination across changes in number-related cues. Most children learned the discrimination and transferred their learning on the basis of relational cues. (Author/CI)

A "proof" is given to show that the set of natural numbers is not countable. (DT)