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INTRODUCTION

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with these applications requires that the teacher and the learner examine the
mathematical principles behind why and how a concept is applied.
content
The content in this reference guide is based on over forty mathematical con-
cepts that are studied in different levels of high school mathematics. For exam-
ple, linear functions are typically learned in algebra and are continually used
beyond calculus. Each of the concepts is listed alphabetically and can be read
independently. This format has been selected for pragmatic purposes, so that the
applications can be used efficiently. Consequently, we occasionally synthesize
concepts, such as referring to slope and derivative as rates, or cross-reference
topics because some applications are based on related or multiple concepts. 
The ideas presented in this book are not a comprehensive account of high
school mathematics nor do they represent every possible application. We do not
feel that every mathematical principle taught in a high school curriculum has a
realistic application. We do feel there are situations where it is necessary to
explore some mathematics that may not be applied. For example, the study of
angles formed by parallel lines does not have many realistic applications, but the
concepts can be used to introduce similarity, a topic with many useful applica-
tions. In addition, the concepts presented here do not introduce every application
of high school mathematics. Our intent is to promote applications about mathe-
matical concepts that are commonly studied in high school mathematics, even
though there are additional interesting connections to other concepts that may not
have as much emphasis in a school’s curriculum. Furthermore, we simply cannot
be aware of all of the applications that have realistic connections to the concepts
we have listed. If you have any additional ideas, please share them with us by
sending an email to .
The depth of description of an application varies within each concept. Some-
times an application will be described in the form of a story, and other times it
will be described in a few sentences to avoid redundancy with a similar analysis
in another section. Sometimes we will just point in the direction of an important
application. Sometimes we will provide a historical, rather than contemporary,
application to show the genesis of a mathematical concept. The amount of math-
ematics described in each of the sections varies, depending on the context and
complexity of the situation. We would much rather provide a flavor of how
mathematics is used than go into detail for every application. In fact, many appli-
cations discussed in this book are based on simplified conditions, even though
the real world often has unusual limitations, constraints, or peculiarities. For
example, we neglect weather conditions when studying the motion of a baseball.
Furthermore, we approximate the shapes of objects, such as assuming that the
earth is a perfect sphere. Simplified situations are used in this reference guide in
order to provide general principles in a concise manner so that the concepts can
be understood by a high school student. World Wide Web references at the end