This paper, a derivation of the multiple correlation formula for unstandardized (raw) scores, is the fourth in a series of publications. The purpose of these papers is to provide supplementary reading for students of applied statistics. The intended audience is social science graduate and advanced undergraduate students familiar with applied…

This paper presents in detail a proof of the limits of the sample bivariate correlation coefficient which requires only knowledge of algebra. Notation and basic formulas of standard (z) scores, bivariate correlation formulas in unstandardized and standardized form, and algebraic inequalities are reviewed first, since they are necessary for…

Proposes a scenario to describe the formation of a planetary nebula, a cloud of gas surrounding a very hot compact star. Describes the nature of a planetary nebula, the number observed to date in the Milky Way Galaxy, and the results of research on a specific nebula. (MDH)

The bilingual dictionary has been adapted from a dictionary originally developed by Teresa Kow and Euphine Cheung in New York to assist Chinese students in their understanding of mathematics vocabulary and concepts in English. A total of 204 terms and definitions are provided in English with Chinese translations directly below the entries. Each…

This material was prepared to help students understand the algebraic process involved in solving mixture problems. The paper copy is designed to be used with a 25-minute audiotape. Students are given a problem which is solved step by step; then they are to answer questions about each step. (MNS)

Looks at one phase of the water cycle; the formation of drops in cooling water vapor. Examines the influence of surface shape on the equilibrium of the liquid and gas phases. Discusses the mathematical formulas that model the phenomenon. (MDH)

Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)

Uses the context of rock climbing to discuss the science concept of friction. Presents the mathematics equations that describe the concept. Examines the physics of different rock climbing situations encountered and equipment used. A series of related problems with answers is provided. (MDH)

The Golden Section, also known as the "Golden Mean" and the "Divine Proportion," is a ratio found in art and nature that has mathematical properties. This book explores these geometric and algebraic properties in a variety of activities. Construction problems, designs using the pentagon and pentagram, and opportunities to work…

Discusses the hydrodynamic reasons why a riverbed meanders through a plain. Describes how water movement at a bend in a river causes erosion and changes in the riverbed. Provides a mathematical model to explain the periodic shape of meanders of a river in a plain. (MDH)

Utilized is the technique of expanding circles to explore the truth of the statement that, if the sums of the lengths of the opposite sides of a quadrilateral are equal, then a circle can be inscribed within that quadrilateral. This statement is the converse of a well-known geometric theorem. (JJK)

One in a series of core instructional materials for apprentices to use during the first or second years of apprenticeship-related subjects training, this booklet deals with basic mathematics. The first section consists of an outline of the content and scope of the core materials as well as a self-assessment pretest. Covered in the three…

This is a supplementary SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include sets, projective geometry, open and closed paths, finite…

Presented are mathematical games in six categories of mathematical objectives: learn the language of mathematics; use mathematical notation; know facts; develop skills; understand concepts; and devise strategies. Numbers of players, rules, and diagrams are provided for each problem. (YP)

Discusses the energy flux-density of two beams of light of equal energy that are intersected at a given angle. Examines an apparent contradiction to the physics law of conservation of energy known as Vavilov's paradox. (MDH)