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

[Kulazo]

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.)

 

[micromass]

What level are you aiming at? If you don't know abstract algebra, then your options are quite limited. But Lang is a decent book on high school level: https://www.amazon.com/dp/0387966544/?tag=pfamazon01-20

One of the best books that deals with the topics you mention is Brannan: https://www.amazon.com/dp/1107647835/?tag=pfamazon01-20 But this requires you to know linear algebra and some group theory.

 

[Kulazo]

What level are you aiming at? If you don't know abstract algebra, then your options are quite limited. But Lang is a decent book on high school level: https://www.amazon.com/dp/0387966544/?tag=pfamazon01-20

One of the best books that deals with the topics you mention is Brannan: https://www.amazon.com/dp/1107647835/?tag=pfamazon01-20 But this requires you to know linear algebra and some group theory.

I have an excellent knowledge of high school 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%20IGCSE/Mathematics%20(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.

 

[bcrowell]

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.

 

[micromass]

The OP is looking for books on high school level. Coxeter is not high school level.

 

[MidgetDwarf]

The OP is looking for books on high school level. Coxeter is not high school level.

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?

 

[verty]

I would just get this book: Barron's E-Z Geometry. It seems to cover what you are missing from the syllabus.

 

[youngstudent16]

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.

 

[Kulazo]

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?

I solved all of them. Do you have any suggestions on what I should read after Kiselev?

 

[econreader]

Is there anything below kislev?

Have a look at Birkhoff and Beatley's Basic Geometry.

 

[MidgetDwarf]

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.

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.

 

[MidgetDwarf]

I solved all of them. Do you have any suggestions on what I should read after Kiselev?

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?

 

[mathwonk]

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.