Geometry Great Trigonometry and geometry books?

[christian0710]

Hi I'm looking for 2 books
1. a big geometry and trigonometry book that covers almost everything (also proofs) from basic to intermediate so i have a solid understanding of geometry trigonometry.
2. a geometry or trigonometry that gives you an appreciation for trigonometry fx how it was used in history, or smart things you can use it for.

So far I've looked at
https://www.amazon.com/dp/055858876X/?tag=pfamazon01-20- Null pearson
https://www.amazon.com/dp/1111826854/?tag=pfamazon01-20

Suggestions are welcomed :)

 

[jedishrfu]

There's a popular book by Jan Gullberg that while not a textbook covers these things well.

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

 

[MidgetDwarf]

Geometry, by Harold Jacobs. Get the 2nd edition. The 3rd edition is watered down. For trig, I prefer Gelfand, however, knowledge of geometry is needed. I would get a standard book, ie David Cohen(buy the pre calculus version it is an algebra and trig book in 1). Stewart Precalculus. (Axler is a better choice but it is kind of rigorous for an introduction)There are better books for gwometry, ie Kisselev planimetry, however there are no answers in the back, and the book is rather terse. This is a recommended 2nd reading.

 

[MidgetDwarf]

Lang also has a neat geometry book, but I would avoid it. It doesn't follow standard euclidean axioms.

 

[John F. Gogo]

Hi I'm looking for 2 books
1. a big geometry and trigonometry book that covers almost everything (also proofs) from basic to intermediate so i have a solid understanding of geometry trigonometry.
2. a geometry or trigonometry that gives you an appreciation for trigonometry fx how it was used in history, or smart things you can use it for.

So far I've looked at
https://www.amazon.com/dp/055858876X/?tag=pfamazon01-20- Null pearson
https://www.amazon.com/dp/1111826854/?tag=pfamazon01-20

Suggestions are welcomed :)

It's all in the proofs. The proofs drove me crazy- and what they meant.

 

[christian0710]

Geometry, by Harold Jacobs. Get the 2nd edition. The 3rd edition is watered down. For trig, I prefer Gelfand, however, knowledge of geometry is needed. I would get a standard book, ie David Cohen(buy the pre calculus version it is an algebra and trig book in 1). Stewart Precalculus. (Axler is a better choice but it is kind of rigorous for an introduction)There are better books for gwometry, ie Kisselev planimetry, however there are no answers in the back, and the book is rather terse. This is a recommended 2nd reading.

The book by Harold Jacobs og Geometry you recommended looks really good based on reviews. Thank you for the recomendation :)
Quick question: What do you mean by "the 3rd edition is washed out?" :)

For trigonometry I'm mostly looking for a big book that covers a lot from fundamentals to more advanced explaining everything clearly (without to many assumptions) but also with some proofs and exercises with answers. I think i might choose Charles P for trigonometry however I've herd it's almost too basic, so Maybe Ron larson is better, don't know yet, tre reviewers on amazon have mixed opinions.

 

[MidgetDwarf]

The book by Harold Jacobs og Geometry you recommended looks really good based on reviews. Thank you for the recomendation :)
Quick question: What do you mean by "the 3rd edition is washed out?" :)

For trigonometry I'm mostly looking for a big book that covers a lot from fundamentals to more advanced explaining everything clearly (without to many assumptions) but also with some proofs and exercises with answers. I think i might choose Charles P for trigonometry however I've herd it's almost too basic, so Maybe Ron larson is better, don't know yet, tre reviewers on amazon have mixed opinions.

Hmm most trigonometry textbooks (the ones used in high school/college) are roughly all the same. I liked David Cohen Pre Calcukus:A Problem Solving Approach. The book is clear, easy to follow, and the exercises are not trivial. The problems are harder than those in Stewart, Larson etc.

Not sure if Simmons wrote a book on trigonometry, but simmons books are good.

About Harold Jacobs. The 3rd edition does away with 2 column proofs, has been made easier. 2nd is better choice. Do not not buy the 3rd ed. It is an inferior book.

I would recommend Gelfand for trig, I believe you have not yet done geometry? You can go through most trig books without a geometry background, however knowledge of geometry is needed for a better understanding. Gelfand takes a geometric method of explaining trigonometry.

It has its problems ofcourse, it is better used as a supplement and later as a reference.

 

[MidgetDwarf]

I know a few people who used Charles P, the found it easier to understand. I read it for about 2 weeks at the school library was easy to read.. A great introduction for the basics. Remember if you fully want to understand a subject (no one does, however one should strive for mastery), multiple readings of differnt books are needed.

 

[KimF]

As to your second question, a classical textbook is S. L. Loney's Plane Trigonometry. It's old, but extremely thorough, and great fun too if you like history.

https://ia802703.us.archive.org/26/items/planetrigonomet00lonegoog/planetrigonomet00lonegoog.pdf

A similar work on spherical trigonometry would be Isaac Todhunter's Spherical Trigonometry.

http://www.gutenberg.org/files/19770/19770-pdf.pdf

In my opinion, there are a few subjects (such as trigonometry and synthethic plane and solid geometry) for which the British textbooks of the 19th century remain unsurpassed.

 

[christian0710]

Hmm most trigonometry textbooks (the ones used in high school/college) are roughly all the same. I liked David Cohen Pre Calcukus:A Problem Solving Approach. The book is clear, easy to follow, and the exercises are not trivial. The problems are harder than those in Stewart, Larson etc.

Not sure if Simmons wrote a book on trigonometry, but simmons books are good.

About Harold Jacobs. The 3rd edition does away with 2 column proofs, has been made easier. 2nd is better choice. Do not not buy the 3rd ed. It is an inferior book.

I would recommend Gelfand for trig, I believe you have not yet done geometry? You can go through most trig books without a geometry background, however knowledge of geometry is needed for a better understanding. Gelfand takes a geometric method of explaining trigonometry.

It has its problems ofcourse, it is better used as a supplement and later as a reference.

I'm definitely going to get Harold Jacobs 2nd Edition. Thank you so much for the recommendation. It's strange how the important stuff (proofs and deeper explanations ) gets trimmed out in newer editions of textbooks, i have heard about this in other books as well.

So maybe If i begin with Harold Jacobs while simultaneously reading Charles P Trigonometry (New or old version?), and then to master trigonometry (I completely agree - mastering a subject and completely understanding it is fun) i might get Gelfand. Does Harold Jacobs do a good job in being clear and introducing subjects without assuming too much? There is also Tutor in a Book's Geometry by Jo Greig But i think it might just be a little too basic for me :)

Which of Simmons books do you recommend? I can see he wrote "Prechaculus mathematics in a nutshell"
Have you heard of Geometry revisited by Coxeter? Looks really good to, might also be of interest for you if you really like geometry :)

 

[micromass]

Have you heard of Geometry revisited by Coxeter? Looks really good to, might also be of interest for you if you really like geometry :)

This is a very difficult book. Certainly not for somebody new to trigonometry.

 

[MidgetDwarf]

As to your second question, a classical textbook is S. L. Loney's Plane Trigonometry. It's old, but extremely thorough, and great fun too if you like history.

https://ia802703.us.archive.org/26/items/planetrigonomet00lonegoog/planetrigonomet00lonegoog.pdf

A similar work on spherical trigonometry would be Isaac Todhunter's Spherical Trigonometry.

http://www.gutenberg.org/files/19770/19770-pdf.pdfIn my opinion, there are a few subjects (such as trigonometry and synthethic plane and solid geometry) for which the British textbooks of the 19th century remain unsurpassed.

Loney is nice, however the OP does not have an understanding geometry and trigonometry. Loney would be better for one who has completed a course on trigonometry, not a beginner.

Its like recommending Apostol/ Spivak as a first calculus book. Both books are excellent and eveyone studying STEM should strive to read themm, howevever, most people will not understand them as a first exposure to a subject. You must learn to crawl before you can run.

 

[christian0710]

Loney is nice, however the OP does not have an understanding geometry and trigonometry. Loney would be better for one who has completed a course on trigonometry, not a beginner.

Its like recommending Apostol/ Spivak as a first calculus book. Both books are excellent and eveyone studying STEM should strive to read themm, howevever, most people will not understand them as a first exposure to a subject. You must learn to crawl before you can run.

Just a quick question: what about Harold Jabobs 1st edition? Is there a reaoson to get 2nd edition instead of 1st?

 

[MidgetDwarf]

Never seen the first. I only recommend books I have personally looked at. Just avoid the 3rd edition like the plague.

 

[christian0710]

Never seen the first. I only recommend books I have personally looked at. Just avoid the 3rd edition like the plague.

Cool I'll try the first edition and see how it is, It's relly cheap in europe. If i dislike it I'll go for the second edition :)