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.

The well-known Frobenius rank inequality established by Frobenius in 1911 states that the rank of the product ABC of three matrices satisfies the inequality rank(ABC) [greater than or equal]rank(AB) + rank(BC) - rank(B) A new necessary and sufficient condition for equality to hold is presented and then some interesting consequences and…

We illustrate the derivations of Jeans' criteria for the gravitational instabilities in a static homogeneous Newtonian system for pedagogical objectives. The critical Jeans density surface is presented in terms of dimensionless sound speeds and (characteristic) length scales. (Contains 1 figure.)

The main purpose of this paper consists in deriving means for making statistical inferences about the distribution of u under the conditions of sigma' is equal to sigma" and sigma' is not equal to sigma". An application of the results to coefficient alpha is appended as an illustration. (CK)

This document gives definitions and symbols for the basic units of measure, for derived units, and for supplementary units. Decimal multiples and sub-multiples of units and units outside the International System also are discussed. Appendix I reproduces the decisions made on units and on the International System by two committees (the General…

This document explains A Programming Language (APL) and describes the experiment that the Information Processing Division has undertaken to introduce APL to the Goddard Scientific Community. A brief historical sketch of steps taken to date is included and appendices giving illustrative examples of how APL actually has been used at the Goddard…

The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

Analyzes National Assessment of Educational Progress data on the computational ability of young adults 26 to 35 years of age. A high percentage of young adults can't balance a checkbook, use an income tax table, or apply simple math concepts in determining unit pricing. (Author/IRT) Aspect of National Assessment (NAEP) dealt with in this document:…

Five different methods for determining the maximizing condition for x(a - x) are presented. Included is the ancient Greek version and a method attributed to Fermat. None of the proofs use calculus. (LS)

A quick estimating tool for determining the approximate cost of equipment from the known cost of similar equipment of a different size or capacity. Cost factors are listed for a variety of equipment. (Author)

Examples of unrealistic'' mathematics and mathematical reasoning are presented and discussed. (DT)

The length of the longest ladder which will go round a right-angled bend in a corridor is found by five methods, none of which involves calculus. (MM)

A counterexample is produced to a conjecture by K. G. Joreskog concerning sufficiency conditions for uniqueness of a restricted factor matrix. A substitute condition is stated and proved for the most common situation where the restricted elements are specified to be zero. (Author)