Computational Looking for a Geometry Proofs Textbook?

[nycmathguy]

I am seeking a geometry proofs textbook. In other words, I seek a textbook that shows all geometric proofs from start to finish. There are books that show proofs worked out as a reference book for students. Can someone provide me with a good geometry book for this purpose? I am particularly interested in the "Statement vs Reason" chart proofs.

Thank you

 

[George Jones]

I am seeking a geometry proofs textbook. In other words, I seek a textbook that shows all geometric proofs from start to finish. There are books that show proofs worked out as a reference book for students. Can someone provide me with a good geometry book for this purpose? I am particularly interested in the "Statement vs Reason" chart proofs.

What type of geometry, and at what level? I ask these questions, because Physics Forums supports posts at the level of high schools students, undergrad students, grad students, and even researchers.

Given your other posts, my guess is that you mean high school Euclidean geometry, and not, for example, the geometry of fibre bundles at the level of a graduate student in mathematics.

 

[nycmathguy]

What type of geometry, and at what level? I ask these questions, because Physics Forums supports posts at the level of high schools students, undergrad students, grad students, and even researchers.

Given your other posts, my guess is that you mean high school Euclidean geometry, and not, for example, the geometry of fibre bundles at the level of a graduate student in mathematics.

I am talking about geometry at the high school level, particularly Euclidean Geometry. I need a book that shows proofs done not so much teaching how to do proofs using the Statements versus Reasons chart.

Thanks...

 

[Mark44]

I seek a textbook that shows all geometric proofs from start to finish. There are books that show proofs worked out as a reference book for students.

As far as I know there is no such book. The last time I taught HS geometry was 1976. The textbook showed some proofs of theorems, from start to finish, but expected the students to use the ideas of the examples to write their own proofs for the problems at the ends of the chapters. If you're looking for a reference book that contains just a bunch of geometry proofs, I think you're probably out of luck.

 

[robphy]

Possibly interesting reading…

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
See page 21 of
A Mathematician’s Lament
by Paul Lockhart

… two-Column proof…

Could anything be more unattractive and inelegant? Could any argument be more obfuscatory and unreadable? This isn’t mathematics! A proof should be an epiphany from the Gods, not a coded message from the Pentagon. This is what comes from a misplaced sense of logical rigor: ugliness. The spirit of the argument has been buried under a heap of confusing formalism.

No mathematician works this way. No mathematician has ever worked this way. This is a complete and utter misunderstanding of the mathematical enterprise. Mathematics is not about erecting barriers between ourselves and our intuition, and making simple things complicated. Mathematics is about removing obstacles to our intuition, and keeping simple things simple.

 

[nycmathguy]

As far as I know there is no such book. The last time I taught HS geometry was 1976. The textbook showed some proofs of theorems, from start to finish, but expected the students to use the ideas of the examples to write their own proofs for the problems at the ends of the chapters. If you're looking for a reference book that contains just a bunch of geometry proofs, I think you're probably out of luck.

Am I really out of luck?

 

[nycmathguy]

Possibly interesting reading…

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
See page 21 of
A Mathematician’s Lament
by Paul Lockhart

Thank you for the link. Check out my reply to Mark44.

 

[Mark44]

Am I really out of luck?

Maybe, based on what you wrote.

I seek a textbook that shows all geometric proofs from start to finish.

The book whose cover you posted looks to be one where the reader does proofs of the examples in it, not one that "shows all geometric proofs from start to finish."

 

[robphy]

Thank you for the link. Check out my reply to Mark44.

Yep.
Enjoy.

• https://www.cut-the-knot.org/geometry.shtml
• https://www.algebra.com/algebra/homework/Geometry-proofs/
• From the author's website:
  S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.
  http://www.mmrc.iss.ac.cn/~xgao/publ.html
• https://www.cs.ru.nl/~freek/100/

 

[nycmathguy]

Yep.
Enjoy.

• https://www.cut-the-knot.org/geometry.shtml
• https://www.algebra.com/algebra/homework/Geometry-proofs/
• From the author's website:
  S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.
  http://www.mmrc.iss.ac.cn/~xgao/publ.html
• https://www.cs.ru.nl/~freek/100/

Thanks again for the extra links.

 

[PeterDonis]

If you're looking for a reference book that contains just a bunch of geometry proofs, I think you're probably out of luck.

Euclid's Elements of Geometry was such a book, but it's not used much as a reference these days (and of course the theorems proved in it are only a subset of theorems known today).

 

[nycmathguy]

Euclid's Elements of Geometry was such a book, but it's not used much as a reference these days (and of course the theorems proved in it are only a subset of theorems known today).

I found a book of worked out geometric proofs. See my reply to Mark44.

 

[mathwonk]

I second the recommendation of Euclid. By far the best geometry book in history, never equaled nor excelled. Very helpful to read in conjunction with Hartshorne's book: Geometry: Euclid and beyond. This assumes you are up to a treatment at the level of an honors math course for young students at a school like berkeley. I taught happily from these books to brlliant 10 year olds one summer in 2011, and also to several classes at UGA.

https://www.greenlion.com/books/EuclidsElements.html

https://www.amazon.com/dp/0387986502/?tag=pfamazon01-20

https://www.math.uga.edu/sites/default/files/inline-files/10.pdf

https://www.amazon.com/dp/1888009187/?tag=pfamazon01-20

https://www.ams.org/notices/200004/fea-hartshorne.pdf

 

[nycmathguy]

Euclid.