Essential Geometry: A Practical Guide
Paper Textbook ($)
Essential Geometry is our introductory geometry text. Written in a clear, easy to read English it covers the fundamental concepts of algebra through a study of variables, sets, linear equations and linear inequalities. Each chapter progressively develops the critical thinking skills necessary for addressing more complex mathematical material through the use of examples and practical applications from fields as diverse as information theory, cartography and physics.
Our approach to course design at this level emphasizes examples over lengthy explanations. Sections start with a brief technical description and a plan English explanation then go into a collection of examples. The examples are selected so that they show not only the basic procedure but also any special cases and unusual situations that a student might encounter.
In the mathematics world, there are two versions of the subject. The "pure" version is extremely abstract. These mathematicians have little interest in real world applications and develop their ideas and theories purely to see where they lead. Applied mathematicians, on the other hand, are explicitly interested in the way mathematica can be used to describe real world situations. The textbooks in our Essentials series take an explicitly practical approach to the material. Applications are briefly discussed at multiple points throughout each chapter and each chapter ends with a project students can do to see how the material is used in real world professions as diverse as art, astronomy and ballistics.
Chapter 1: Ballistics Ballistics is the study of how projectiles move after they've been fired. In this application, students experimentally determine the firing angle that sense a projectile the greatest distance.
Chapter 2: Geometric Constructions Classical Greek geometers developed methods for constructing a variety of geometric objects using just a compass and straightedge. This section covers the procedures for constructing perpendicular bisectors, angle bisectors and parallel lines.
Chapter 3: Surveying This application uses properties of right triangles to calculate the distance between two inaccesible points.
Chapter 4: Tilings Throughout history artists have experimented with the ways that tiles can be arranged to artistically cover a flat surface. This section introduces students to the geometry behind the ways that tiles can be arranged.
Chapter 5: Projections Some historians have subjected that the ability to project an image onto a canvas was a significant factor in Renaissance painting and drawing. This project describes how to create a projection device similar to ones that may have been used during the Renaissance.
Chapter 6: Celestial Navigation If you view the sky as a giant hemisphere then the properties of circles can be used to determine a person's latitude based on some simple observations.
Chapter 7: Volumes of Irregular Solids In this section, we discuss a variety of formulas that can be used to find the volumes of regular objects like prisms and spheres. This application demonstrates a method for finding the volume of irregular objects.