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Geometry What's a good book on geometry to read after Kiselev?

  1. Aug 3, 2015 #1
    I have finished reading both books on geometry by Kiselev and now look to move on but can't find any book to let me do so.

    Specifically, I would like a nice comprehensive book that goes into detail on transformations, isometries, coordinate geometry, symmetry, mensuration, and vectors. Now I'll be realistic and say that such a book may not exist, but it is fine if you can suggest a series of books which cover all of the topics I mentioned, in great detail.

    (Hartshorne's book requires me to read Euclid and I don't want to do so for various reasons, and it also requires an understanding of abstract algebra which ofcourse I don't know a bit of. And on a first glance, it also seems not to cover the topics I mentioned.)
  2. jcsd
  3. Aug 3, 2015 #2
  4. Aug 3, 2015 #3
    I have an excellent knowledge of highschool algebra and was thinking to brushup on Geometry, comprehensively. I want a book (or a series of books) which covers the topics listed for all types of Geometry (coordinate, mensuration...etc) here: http://papers.xtremepapers.com/CIE/Cambridge IGCSE/Mathematics (0580)/0580_y16_sy.pdf (starts on page 24)

    I know this is a thread on geometry but you sound quite knowledgeable. If you're in a generous mood, perhaps you can give me a long (or short) list of books that would cover all of the syllabus listed on that file. I would really really appreciate it.
  5. Aug 3, 2015 #4


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    I'm not familiar with Kiselev, but a couple of possibilities to consider would be:

    Coxeter, Introduction to geometry

    Coxeter, Geometry revisited

    "Introduction to geometry" is a wonderful book.
  6. Aug 3, 2015 #5
    The OP is looking for books on high school level. Coxeter is not high school level.
  7. Aug 4, 2015 #6
    If he has worked through Kisselev, both volumes, then he has a very good understanding of high school geometry and he should move on. Maybe try to find a book on non-euclidean geometries?

    By read, do you mean solved most of the problems? Or did you just attempt a few?
  8. Aug 4, 2015 #7


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    I would just get this book: Barron's E-Z Geometry. It seems to cover what you are missing from the syllabus.
    Last edited: Aug 4, 2015
  9. Aug 4, 2015 #8
    Is there anything below kislev? I have no problem with reading it(its enjoyable even) and about 60% of the problems but some of then proofs are quite difficult for me. It seems some of the problems are fine but then some require creativity and intuition I lack. I had a weak geometry education in middle school.
  10. Aug 4, 2015 #9
    I solved all of them. Do you have any suggestions on what I should read after Kiselev?
  11. Aug 4, 2015 #10
    Have a look at Birkhoff and Beatley's Basic Geometry.
  12. Aug 4, 2015 #11
    Jacobs geometry. It is a step below kiselev. Work through jacobs then follow it up with kis' ev.

    Buy the 1st or 2nd ed of jacobs. Avoid the 3rd and higher.
  13. Aug 4, 2015 #12
    Not sure, zorry. I have weak geometry. I need to practice it more. Maybe Pedeo: A comprehensive course in geometry. I not sure the level of this book. Ask micromass or mathwonk.

    Have you done any other math? Calculus, linear, discrete?
  14. Aug 5, 2015 #13


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    Well I was going to recommend Euclid as the best ,but he is biased against Euclid for some reason. Also Hartshorne in combination with Euclid, seems to me the natural thing to follow Kiselev. I.e. in Kiselev he has learned much of the more basic content of Euclid, just not as deeply as he would in Euclid and Hartshorne. I.e. Kiselev uses real numbers as a crutch to avoid the deep theories of proportion and area in Euclid and Hartshorne.
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