An Introduction to Transformation Geometry

Until recent years the content of most high school geometry courses was essentially the same from school to school. Proof, congruence\u27s, constructions, and similarity were core concepts, taught on the basis of the Euclidean approach. Now, even at the secondary level, students are investigating some aspects of non-Euclidean geometry and learning methods of solving geometric problems different from the traditional methods based on Euclid. Currently we are being told that teaching is no longer a matter of imparting facts and developing certain skills. Our essential task as teachers is to teach each individual how to teach himself in order that he might continue his education long after he has finished formal schooling. Our rapidly changing culture and technology make this imperative. The young person of today may have to prepare himself for several different kinds of occupations in the course of a lifetime as previous ones become obsolete, unfulfilling, or yield too little financially. Releasing our students from the narrow confines of the traditional geometry course is a matter of keeping with the times mathematically. Happily students are now spared the illusion that the Euclidean approach is all there is to geometry. At the end of a year of study, they should have less of a sense of having completed a course in geometry. The inclusion of even a few new topics should reveal to then that many doors are yet to be opened. This introduction is just a glimpse into one of the fascinating areas of modern geometry. The material is presented somewhat in the style of a programmed text, though answers are separate from the text itself. The units may be used for individualized study with answers available to the student, or explored by an entire class guided by the teacher. Some teachers may prefer to have a group of students work individually on certain units and meet as a class for other units. The format should facilitate any one of these approaches . It is hoped that the informality of the discussion as well as the checkpoints and varied exercises make it appealing to the student..