1
$\begingroup$

I am looking for a good resource (preferably in the form of textbooks) for coordinate geometry. Rather than a comprehensive coverage of topics, I am looking more for depth in a particular topic. It is all right if multiple textbooks are required to cover the whole of coordinate geometry (for instance, a book for each of the conic sections).

More than theory, I would like textbooks with insightful problems in the form of unsolved as well as solved examples. I find I can learn theory better through solving problems.

$\endgroup$
1
$\begingroup$

You may want to check out the old school textbooks:

  • Salmon, George. A Treatise on the Analytic Geometry of Three Dimensions. Dublin, 1882.
  • Sommerville, Duncan M'Laren Young. Analytical geometry of three dimensions. The University Press, 1934.
  • J. G. Semple and L. Roth. Introduction to algebraic geometry. Oxford, 1949.

Usually, these classic authors didn't like drawing pictures, and they didn't have the idea of matrix (which comes much later). So I'm not sure if you would like them. On the other hand, modern geometry books become much more abstract, and they don't necessarily mention the classic elementary results.

Personally, I find using matrix helps me a lot in understanding geometry. I benefit a lot from trying to assign geometric meaning to every word in the vocabulary of standard linear algebra and matrix analysis. The book that helps me most is:

  • Pottmann, Helmut, and Johannes Wallner. Computational line geometry. Springer Science & Business, 2009.

A much easier but equally helpful book is:

  • Boehm, Wolfgang, and Hartmut Prautzsch. "Geometric concepts for geometric design." (1994).

Finally, I don't really think coordinate geometry is that important, because too often the geometric meaning is lost in computation with coordinates. It is more intuitive, geometric meaningful to use geometric algebra, which is equivalent to coordinate geometry with a little bit of representation theory.

$\endgroup$
  • $\begingroup$ @Gerard Was that you who downvoted me? I will delete the answer in that case. $\endgroup$ – Troy Woo Jan 11 '15 at 18:31
  • 1
    $\begingroup$ Do these older texts use language that is no longer used today? If so, I think one would need a very strong justification for reading them, especially as a recommendation to someone who is uninitiated in the subject. $\endgroup$ – RghtHndSd Jan 11 '15 at 18:40
  • $\begingroup$ @RghtHndSd Its not that they use some quite different language, but that they focused on classic results, which take you for example, will not be interested in. Classic books is about training your geometry intuition and are probably the right ones for yours so called "uninitiated" people. $\endgroup$ – Troy Woo Jan 11 '15 at 18:48
  • $\begingroup$ I am curious how you know what I am and am not interested in. I also can't tell if "Its not that they use some quite different language" means that they use the same language that is in use today, or if you are saying that this isn't important. $\endgroup$ – RghtHndSd Jan 11 '15 at 23:34
  • $\begingroup$ @TroyWoo: No, I didn't downvote your answer. I appreciate your help and will definitely check out the books. However, it seems that the books you have suggested start at an advanced level. Ideally, I want a book that starts with the fundamentals and subsequently builds up to the desired level. $\endgroup$ – Gerard Jan 12 '15 at 6:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.