Introduction

This electronic book Journey Companion is intended as a supplement to the text Journey into Geometries by Marta Sved published by the Mathematical Association of America. For the past two or three years I have used the text by Sved in the College Geometry course which I teach.

Sved's entertaining book is written as a "trialog" between Alice, Lewis Carrol (the main character and author of Through the Looking Glass and Alice in Wonderland), and Dr. Whatif (a visitor from the 20th century). My classes have read the text and then given formal proofs of some of the results found there.

Chapter 0 is an introduction to techniques of proof in geometry.  While this chapter does not directly correspond to the Sved book, the particular theorems used to illustrate the proof techniques also provide many of the basic geometric facts needed when reading the Sved textbook. In this chapter the proofs of the theorems are mine.

Chapters 1 and beyond consist of material distilled from the corresponding chapter of the Sved book restated in formal theorem, definition format. The formal proofs of these theorems are the work of the students in the class. Occasionally I wanted to illustrate a point and contributed the proof of a theorem, but those instances are few and far between. Virtually all the proofs are student work.

This semester (Fall 1997) is the first time the materials have been produced as html documents and put on the web. We have used the editor provided by Netscape. Previous classes produced Maple documents. Current students have had the Maple documents as well as the Sved text for reference, so the work here is also due in part to the efforts of previous classes, although most of it is reworked. All classes have produced diagrams using Geometer's Sketchpad (GSP) software.

Careful writing suitable for publication takes time and so only the first two chapters of the Sved book currently have corresponding chapters in the Journey Companion. Perhaps future classes will add more.

Comments and suggestions are invited and can be sent to: Bryan Dorner at dornerbc@plu.edu.

Table of Contents | Chapter 0