The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

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.

Twenty classes in ten schools with 627 sixth-grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One-way ANOVA analysis indicate that significant difference…

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

Analyzed construction of approximative expressions with two numerals in Dutch. Found that choice of number words was not arbitrary and that various kinds of factors are involved. Results suggest that analogue magnitude code is used in estimating and comparing, and human cognition seems to be able to perform simple calculations with quantities,…

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

Everyone is familiar with the concept that the cube and octahedron, dodecahedron and icosahedron are dual pairs, with the tetrahedron being self-dual. On the face of it, the concept seems straightforward; however, in all but the most symmetrical cases it is far from clear. By using the computer and three-dimensional graphics programs, it is…