Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

The paper shows how to find the min and max extreme interval values for the exponential and triangular distributions from the min and max uniform extreme interval values. Tables are provided to show the min and max extreme interval values for the uniform, exponential, and triangular distributions for different probabilities and observation sizes.

The standard for measuring fuel efficiency in the U.S. has been miles per gallon (mpg). However, the Environmental Protection Agency's (EPA) switch in rating fuel efficiency from miles per gallon to gallons per hundred miles with the 2013 model-year cars leads to interesting and relevant mathematics with real-world connections. By modeling…

This study aims at exploring processes of flexibility and coordination among acts of visualization and analysis in students' attempt to reach a general formula for a three-dimensional pattern generalizing task. The investigation draws on a case-study analysis of two 15-year-old girls working together on a task in which they are asked to calculate…

A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a…

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…

Demonstrates the logical relationship between percentage composition and an empirical formula using a technique that depends on determining a minimum molar mass for the compound based on the mass percent of each element. (DDR)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

The dynamics of some common sports, such as race walking, running, cycling, jumping, and throwing, are presented. Rough estimates of the relevant physical quantities required for these individual sports are discussed. General mathematical formulas are derived which can be used for judging the performance of any athlete. (Author/KR)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

This article presents 12 examples of the use of a calculator in the algebra class. The calculator codes and the mathematical formulas of the examples are presented in the appendix. (Author/YP)

The rule of 78 is used by banks and loan companies to compute the amounts due when installment loans are paid early. Describes an unexpected case of negative amortization when the rule is applied. Presents an actual problem and discusses the case. (YP)

This project involves devising and evaluating a sales tax schedule to meet the specific revenue needs of a hypothetical state in the United States. Conducting this unit involves many mathematical skills in a learning environment familiar to the student. The essential parts of the project consist of student preparation of a tax schedule and class…