Geometry: A High School Course

by Serge Lang, Gene Murrow

From the "A prominent research mathematician and a high school teacher have combined their efforts in order to produce a high school geometry course. The result is a challenging, vividly written volume which offers a broader treatment than the traditional Euclidean one, but which preserves its pedagogical virtues. The material included has been judiciously some traditional items have been omitted, while emphasis has been laid on topics which relate the geometry course to the mathematics that precedes and follows. The exposition is clear and precise, while avoiding pedantry. There are many exercises, quite a number of them not routine. The exposition falls into twelve 1. Distance and Angles.- 2. Coordinates.- 3. Area and the Pythagoras Theorem.- 4. The Distance Formula.- 5. Some Applications of Right Triangles.- 6. Polygons.- 7. Congruent Triangles.- 8. Dilatations and Similarities.- 9. Volumes.- 10. Vectors and Dot Product.- 11. Transformations.- 12. Isometries.This excellent text, presenting elementary geometry in a manner fully corresponding to the requirements of modern mathematics, will certainly obtain well-merited popularity. Publicationes Mathematicae Debrecen#1

Genres: Mathematics, Textbooks, Geometry

406 pages, Kindle Edition

First published February 19, 1987

About the author

Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Librarian Note: There is more than one author in the GoodReads database with this name. See this thread for more information.

Reviews

[Shahad Zawinski · Rating 4 out of 5]

I will surely accept that this may change you thinking as well

[Joseph Kulisics · Rating 4 out of 5]

I think that the book is a good treatment of the subject, but I'm guessing that the formalization could be handled with a little more care without sacrificing the important aspects of the presentation, the connection of geometry to analytic methods as explored in the dot product chapters and other sections of the book. For example, there seems to me to be some lack of rigor when comparing say, Hilbert's Foundations of Geometry, with the axiomatic basis in the book. (I could be missing something, but some facts, like the number of points in which a line can intersect a circle and the circumstances of each type of intersection, are either not a consequence of the book's axioms or require more sophisticated proofs than could be supplied in the book. In the first case, augmenting the axiomatic basis might have made sense and allayed any student concerns about missing axioms, and in the second case, at least acknowledging that the consequences, which were critically important to solving some problems because the problems basically required looking at a figure whose major features required justification, were provably true but required some skill.) In any case, I understand that there are similar problems in Euclid's original treatment of geometry. Maybe contemplating a model's shortcomings is of value, too. The peculiar value of the presentation of this book is not in its model perfection but in its introduction to rigorous proof and in the connections that the text makes between geometry and analytic topics. In making connections between the geometry and analytic methods and as a good introduction to proof, the text is a major success, and I can't recommend it enough.