Math Without Borders Geometry

Although the hard copy versions of this textbook are now out of print, I have made a special arrangement with the authors and have been granted permission to distribute the text in electronic form. The full text, in pdf format, is included with the course materials on the distribution flash drive. It does not require a separate purchase.

This arrangement not only lowers the cost of the course to you, it will enable this exceptional text to stay in publication for the long term. If you find a printed copy (with any publication date) be assured that the content has remained the same over all printings. However, you will not need to purchase a printed copy to get full value from this course.

Geometry: A Guided Inquiry is a very special textbook!

Of all the geometry texts I have used over the past 35 years, this one stands out as by far the richest, most intuitive, and most interesting. This text is unique. (See the review on mathmammoth.com.)

• Most geometry textbooks present a long list of facts about geometric figures organized in a rigid logical order, working generally from simple to more complex. Applications of these facts may or may not be made clear to the student. Geometry: A Guided Inquiry is different.  It starts each chapter by posing an interesting geometric problem (puzzle), called the “Central Problem” for the chapter. Clusters of geometric facts are introduced, as needed, in the process of solving these problems. The usefulness and relevance of the new facts are therefore apparent from the moment they are first presented.
• Most geometry textbooks, especially those written under the influence of the “New Math” era of the 1960s, put heavy emphasis on precise use of technical vocabulary and mathematical notation.Geometry: A Guided Inquiry emphasizes the underlying geometric and mathematical ideas and works to help the student understand them intuitively as well as logically. Overemphasis on technical vocabulary and complex notation can actually stand in the way of understanding, so the authors use simplified vocabulary and notation wherever possible.
• Most geometry textbooks start each problem set with lots of routine, repetitive problems, gradually working up to an interesting problem or two at the end of the assignment. Geometry: A Guided Inquiry puts the best problems right up front! From the very beginning the student is given problems worth solving.
• Most geometry textbooks read like they were written by a committee following a prescribed agenda. Most in fact are! The life is squeezed out of the narrative in the process. Geometry: A Guided Inquiry has a distinct sense of authorship. The authors are good mathematicians, good teachers, and good writers. Their joy in the pursuit of mathematics shows through in their writing.

Geometry: A Guided Inquiry makes frequent use of compass, protractor and ruler activities, data tables, guess and check methods, model-building, and other techniques of intuitive exploration in preparation for general solutions. (The GeoGebra activities add a new dimension to the opportunities for exploration with dynamic illustrations.) Each chapter begins with a “Central Problem” that provides the focus and motivates the discussion in that chapter. The Central section presents all the essential new material. Along the way the student is led to a solution of the Central Problem, while exploring its connections with other topics. After the Central section is a Review section, and each of the first seven chapters are followed with a short Algebra Review that stresses algebra topics related to the current work.

Next comes the best part. Each chapter has an open ended Projects section with problems that are extensions to the material in the Central section, sometimes carrying the discussion in new directions. (The Project sections include some of the most interesting material in the text!) In a classroom setting, where students work at their own pace, the quicker students would work on the Project section while the slower students finish the Central and Review sections. In a home study environment the student should read through the whole Project section and work on as many of the project problems as possible within the time frame available. Students who find the work easy, rather than going faster, you should instead take more time and go deeper!

The textbook is available as a digital book (consisting of pdf files, chapter by chapter) that are now distributed together with the course materials. Since the format and style of this text will be new to most of you, here are some sample chapters:

Table of Contents / Chap 1 (Shortest Path Problem) / Chap 5 (Constructions)

The Home Study Companion: Geometry course supplements the textbook in several important ways:

• It has a video introduction to each chapter which gives a chapter overview.
• It provides complete, worked out solutions (not just answers) to all problems in the Central and Project sections of the text.
• The pdf solution manual also contains additional commentary to supplement the presentation of the text. Be sure to read through the solution guide after working through the chapter to get this additional commentary.
• It provides a collection of hundreds of demonstrations using GeoGebra, covering most of the main concepts, and many additional explorations, in the Central and Projects sections of each chapter. Accompanying each demonstration, or cluster of demonstrations, is an activity guide that will help you get the most out of the GeoGebra explorations and teach you how to use GeoGebra as a tool on your own as well.
• Geometry: A Guided Inquiry was written long before the current obsession with standardized testing, and it marches to a different drummer. It covers many fascinating topics you will see in no other high school Geometry textbook. The selection of topics in the text is excellent, but the authors’ choice of topics (in 1970) did not anticipate every choice of the various state standards committees at the end of the century. Therefore the Home Study Companion adds Extensions to the chapters, as needed, to cover these additional topics. (Students not affected by mandatory statewide testing can treat the extensions as optional topics, but they are actually good topics, so it is recommended that they be covered.)

GeoGebra

I have created dynamic geometry demonstrations for most of the concepts in the text using GeoGebra, a free, downloadable, cross-platform program (download here). Anyone who would like to get a feel for GeoGebra (even if you are not currently studying Geometry), can download the program now and visit GeoGebratube.org for demonstrations and activities I have shared with the public. (Explore GeoGebratube for many more demonstrations created by others as well.)