This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

Automatic processing of 2-digit numbers was demonstrated using the size congruency effect (SiCE). The SiCE indicates the processing of the irrelevant (numerical) dimension when 2 digits differing both numerically and physically are compared on the relevant (physical) dimension. The SiCE was affected by the compatibility between unit and decade…

Logarithmic spirals are among the most fascinating curves in the plane, being the only curves that are equiangular, and the only ones that are self-similar. In this article, we show that in three dimensions, these two properties are independent. Although there are surfaces that have both properties, there are some that are equiangular, but not…

This article is about a very small subset of the positive integers. The positive integer N is said to be "perfect" if it is the sum of all its divisors, including 1, but less that N itself. For example, N = 6 is perfect, because the (relevant) divisors are 1, 2 and 3, and 6 = 1 + 2 + 3. On the other hand, N = 12 has divisors 1, 2, 3, 4 and 6, but…

In this note, a modified Second Derivative Test is introduced for the relative extrema of a single variable function. This improved test overcomes the difficulty of the second derivative vanishing at the critical point, while in contrast the traditional test fails for this case. A proof for this improved Second Derivative Test is presented,…

Tables and charts are efficient tools for organizing numbers, but many people give little consideration to the order in which they present the data. This article illustrates the strengths and weaknesses of four criteria for organizing data--empirical, theoretical, alphabetical and a standardized reporting scheme.

In this paper, some new results related to the integral mean value theorem are proven. This paper includes a discussion of Flett's Mean Value Theorem. (Contains 2 figures.)

Several proofs demonstrating that there are infinitely many primes, different types of primes, tests of primality, pseudo primes, prime number generators and open questions about primes are discussed in Section 1. Some of these notions are elaborated upon in Section 2, with discussions of the Riemann zeta function and how algorithmic complexity…

This short note demonstrates that even for smaller natural numbers, one can have some rule to follow when it comes to studying the divisibility by 4 and 8. One need not actually divide the number.

The varied forms and semantic factors of Japanese ordinal expressions are related to one another in a coherent system. In Japanese, the cardinal number form is a numeral compound in construction with a referent. The numeral compound consists of a number and a numeral adjunct. Numeral adjuncts are derived from bound forms, or numeral suffixes, and…

This publication is part of a series of guides written by Pennsylvania's Department of Public Instruction and is designed to present some of the unifying concepts in mathematics to elementary teachers. This pamphlet discusses the commutative, associative, and closure properties for addition and multiplication of whole numbers, and the distributive…

Projects that involve counting real things either from 1 to 100 or from 1 to 1000 are presented. The projects encourage children's guessing, ordering numbers, recording results in a variety of ways, counting elements of a subset as well as the entire set, and some problem solving. (MN)

Examples are given of several compound games of strategy that involve mathematical theory and provide new bases for understanding and axiomatizing the concept of "number." (MN)

Some patterns in prime numbers and their implications for general theorems are presented. Much of the material is taken from "The Strong Law of Small Numbers," an unpublished paper by Richard Kenneth Guy. (MP)