The bible of geometry: Is there a modern treatment of geometries from the most primitive to the most advanced?What is the modern axiomatization of (Euclidean) plane geometry?Obtaining a deeper understanding of lower level MathematicsFrom the viewpoint of modern geometry, is there a “best” definition of the term “triangle”?Bridging the gap between classical and modern projective geometryWhat's the most general geometry branch?I need a good reading list of the Masterworks of mathematics.Out of those geometries below, which one is the most general?Reading old books by the mastersGeometry textbooks from the 1800sis there book like 'PROOF FROM THE BOOK'?
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The bible of geometry: Is there a modern treatment of geometries from the most primitive to the most advanced?
What is the modern axiomatization of (Euclidean) plane geometry?Obtaining a deeper understanding of lower level MathematicsFrom the viewpoint of modern geometry, is there a “best” definition of the term “triangle”?Bridging the gap between classical and modern projective geometryWhat's the most general geometry branch?I need a good reading list of the Masterworks of mathematics.Out of those geometries below, which one is the most general?Reading old books by the mastersGeometry textbooks from the 1800sis there book like 'PROOF FROM THE BOOK'?
$begingroup$
About 2000 years ago Euclid wrote a book that contains (almost) all the geometry that was known at his time. Today, in the 21st century, our knowledge of geometry increased drastically: our knowledge of euclidean geometry is better and we have better foundations. Also we have so many (interlinked) branches of geometry:
- Euclidean geometry
- Neutral geometry
- Affine geometry
- Vector geometry
- Analytic geometry
- Non euclidean geometry
- Projective geometry
- Discrete geometry
- Differential geometry
- Integral geometry
- Algebraic geometry
- Discrete differential geometry
- Combinatorial geometry
- Computational geometry
- Symplectic geometry
- Kahlerian geometry
- Complex geometry
- Descriptive geometry
- Diophantine geometry
- Metric geometry
- Convex geometry
- Noncommutative geometry
- Nonriemanniann geometry
- Arithmetic geometry
- Topology
Did anyone try to do today what Euclid did long ago. I understand this is impossible for one person, but a group of specialists can do it. I'm not asking for an encyclopedic work but for a treatment of geometries from the most primitive to the most advanced. It will span thousands of pages but perhaps it will be the best work on geometry for the centuries to come. Does anyone have this idea? If Dieudonne alone could do a treatment of analysis in 10+ volumes, a group of mathematicians can do it.
geometry book-recommendation
edited Apr 21 at 18:33
Blue
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
$endgroup$
|
show 4 more comments
$begingroup$
About 2000 years ago Euclid wrote a book that contains (almost) all the geometry that was known at his time. Today, in the 21st century, our knowledge of geometry increased drastically: our knowledge of euclidean geometry is better and we have better foundations. Also we have so many (interlinked) branches of geometry:
- Euclidean geometry
- Neutral geometry
- Affine geometry
- Vector geometry
- Analytic geometry
- Non euclidean geometry
- Projective geometry
- Discrete geometry
- Differential geometry
- Integral geometry
- Algebraic geometry
- Discrete differential geometry
- Combinatorial geometry
- Computational geometry
- Symplectic geometry
- Kahlerian geometry
- Complex geometry
- Descriptive geometry
- Diophantine geometry
- Metric geometry
- Convex geometry
- Noncommutative geometry
- Nonriemanniann geometry
- Arithmetic geometry
- Topology
Did anyone try to do today what Euclid did long ago. I understand this is impossible for one person, but a group of specialists can do it. I'm not asking for an encyclopedic work but for a treatment of geometries from the most primitive to the most advanced. It will span thousands of pages but perhaps it will be the best work on geometry for the centuries to come. Does anyone have this idea? If Dieudonne alone could do a treatment of analysis in 10+ volumes, a group of mathematicians can do it.
geometry book-recommendation
edited Apr 21 at 18:33
Blue
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
$endgroup$
2
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
3
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
$endgroup$
– Euclidos
Apr 21 at 15:50
$begingroup$
Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
$endgroup$
– Aminopterin
Apr 21 at 18:41
4
$begingroup$
Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
$endgroup$
– Eric Wofsey
Apr 21 at 19:57
|
show 4 more comments
$begingroup$
About 2000 years ago Euclid wrote a book that contains (almost) all the geometry that was known at his time. Today, in the 21st century, our knowledge of geometry increased drastically: our knowledge of euclidean geometry is better and we have better foundations. Also we have so many (interlinked) branches of geometry:
- Euclidean geometry
- Neutral geometry
- Affine geometry
- Vector geometry
- Analytic geometry
- Non euclidean geometry
- Projective geometry
- Discrete geometry
- Differential geometry
- Integral geometry
- Algebraic geometry
- Discrete differential geometry
- Combinatorial geometry
- Computational geometry
- Symplectic geometry
- Kahlerian geometry
- Complex geometry
- Descriptive geometry
- Diophantine geometry
- Metric geometry
- Convex geometry
- Noncommutative geometry
- Nonriemanniann geometry
- Arithmetic geometry
- Topology
Did anyone try to do today what Euclid did long ago. I understand this is impossible for one person, but a group of specialists can do it. I'm not asking for an encyclopedic work but for a treatment of geometries from the most primitive to the most advanced. It will span thousands of pages but perhaps it will be the best work on geometry for the centuries to come. Does anyone have this idea? If Dieudonne alone could do a treatment of analysis in 10+ volumes, a group of mathematicians can do it.
geometry book-recommendation
edited Apr 21 at 18:33
Blue
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
$endgroup$
About 2000 years ago Euclid wrote a book that contains (almost) all the geometry that was known at his time. Today, in the 21st century, our knowledge of geometry increased drastically: our knowledge of euclidean geometry is better and we have better foundations. Also we have so many (interlinked) branches of geometry:
- Euclidean geometry
- Neutral geometry
- Affine geometry
- Vector geometry
- Analytic geometry
- Non euclidean geometry
- Projective geometry
- Discrete geometry
- Differential geometry
- Integral geometry
- Algebraic geometry
- Discrete differential geometry
- Combinatorial geometry
- Computational geometry
- Symplectic geometry
- Kahlerian geometry
- Complex geometry
- Descriptive geometry
- Diophantine geometry
- Metric geometry
- Convex geometry
- Noncommutative geometry
- Nonriemanniann geometry
- Arithmetic geometry
- Topology
Did anyone try to do today what Euclid did long ago. I understand this is impossible for one person, but a group of specialists can do it. I'm not asking for an encyclopedic work but for a treatment of geometries from the most primitive to the most advanced. It will span thousands of pages but perhaps it will be the best work on geometry for the centuries to come. Does anyone have this idea? If Dieudonne alone could do a treatment of analysis in 10+ volumes, a group of mathematicians can do it.
geometry book-recommendation
geometry book-recommendation
edited Apr 21 at 18:33
Blue
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
edited Apr 21 at 18:33
Blue
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
edited Apr 21 at 18:33
Blue
49.8k970158
edited Apr 21 at 18:33
Blue
49.8k970158
edited Apr 21 at 18:33
Blue
49.8k970158
49.8k970158
asked Apr 21 at 15:25
EuclidosEuclidos
313
asked Apr 21 at 15:25
EuclidosEuclidos
313
asked Apr 21 at 15:25
EuclidosEuclidos
313
313
2
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
3
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
$endgroup$
– Euclidos
Apr 21 at 15:50
$begingroup$
Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
$endgroup$
– Aminopterin
Apr 21 at 18:41
4
$begingroup$
Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
$endgroup$
– Eric Wofsey
Apr 21 at 19:57
|
show 4 more comments
2
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
3
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
$endgroup$
– Euclidos
Apr 21 at 15:50
$begingroup$
Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
$endgroup$
– Aminopterin
Apr 21 at 18:41
4
$begingroup$
Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
$endgroup$
– Eric Wofsey
Apr 21 at 19:57
2
2
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
3
3
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
$endgroup$
– Euclidos
Apr 21 at 15:50
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
$endgroup$
– Euclidos
Apr 21 at 15:50
$begingroup$
Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
$endgroup$
– Aminopterin
Apr 21 at 18:41
$begingroup$
Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
$endgroup$
– Aminopterin
Apr 21 at 18:41
4
4
$begingroup$
Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
$endgroup$
– Eric Wofsey
Apr 21 at 19:57
$begingroup$
Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
$endgroup$
– Eric Wofsey
Apr 21 at 19:57
|
show 4 more comments
2 Answers
2
active
oldest
votes
$begingroup$
I can't give a universal answer but if you are interested in the unification of several areas of geometry and group theory I would highly recommend "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger.
The book covers a vast number of topics in metric and Riemannian geometry as well as their connections to geometric group theory.
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
$endgroup$
add a comment |
$begingroup$
Marcel Berger's two volume Geometry (https://books.google.com.mt/books/about/Geometry_I.html?id=5W6cnfQegYcC&redir_esc=y ) might be close to what you're looking for. As you note, the subject is now vast and so the books are not comprehensive, but they definitely give an introduction to many of the areas.
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
$endgroup$
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I can't give a universal answer but if you are interested in the unification of several areas of geometry and group theory I would highly recommend "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger.
The book covers a vast number of topics in metric and Riemannian geometry as well as their connections to geometric group theory.
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
$endgroup$
add a comment |
$begingroup$
I can't give a universal answer but if you are interested in the unification of several areas of geometry and group theory I would highly recommend "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger.
The book covers a vast number of topics in metric and Riemannian geometry as well as their connections to geometric group theory.
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
$endgroup$
add a comment |
$begingroup$
I can't give a universal answer but if you are interested in the unification of several areas of geometry and group theory I would highly recommend "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger.
The book covers a vast number of topics in metric and Riemannian geometry as well as their connections to geometric group theory.
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
$endgroup$
I can't give a universal answer but if you are interested in the unification of several areas of geometry and group theory I would highly recommend "Metric Spaces of Non-Positive Curvature" by Bridson and Haefliger.
The book covers a vast number of topics in metric and Riemannian geometry as well as their connections to geometric group theory.
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
answered Apr 21 at 17:53
Sam HughesSam Hughes
839114
839114
add a comment |
add a comment |
$begingroup$
Marcel Berger's two volume Geometry (https://books.google.com.mt/books/about/Geometry_I.html?id=5W6cnfQegYcC&redir_esc=y ) might be close to what you're looking for. As you note, the subject is now vast and so the books are not comprehensive, but they definitely give an introduction to many of the areas.
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
$endgroup$
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
add a comment |
$begingroup$
Marcel Berger's two volume Geometry (https://books.google.com.mt/books/about/Geometry_I.html?id=5W6cnfQegYcC&redir_esc=y ) might be close to what you're looking for. As you note, the subject is now vast and so the books are not comprehensive, but they definitely give an introduction to many of the areas.
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
$endgroup$
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
add a comment |
$begingroup$
Marcel Berger's two volume Geometry (https://books.google.com.mt/books/about/Geometry_I.html?id=5W6cnfQegYcC&redir_esc=y ) might be close to what you're looking for. As you note, the subject is now vast and so the books are not comprehensive, but they definitely give an introduction to many of the areas.
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
$endgroup$
Marcel Berger's two volume Geometry (https://books.google.com.mt/books/about/Geometry_I.html?id=5W6cnfQegYcC&redir_esc=y ) might be close to what you're looking for. As you note, the subject is now vast and so the books are not comprehensive, but they definitely give an introduction to many of the areas.
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
answered Apr 21 at 15:44
postmortespostmortes
2,58531523
2,58531523
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
add a comment |
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
I actually have these books, haven't read them yet. They treat geometry abstractly. I was searching for a treatment that starts from elementary (axioms, angles, congruent triangles...) to reach the more advanced theorems and the abstract treatment a la Marcel Berger.
$endgroup$
– Euclidos
Apr 21 at 15:48
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
$begingroup$
Euclid himself wrote other books on geometry and he left out much that was already known. Read the Wikipedia ariticle Euclid for more details. You should ask a more modest and revised question because what you asked for does not exist.
$endgroup$
– Somos
Apr 21 at 17:49
add a comment |
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2
$begingroup$
Bourbaki, perhaps?
$endgroup$
– kimchi lover
Apr 21 at 15:31
3
$begingroup$
Actually, yes, you are asking for an encyclopedic treatment. As far as I know, there is no such thing. The most comprehensive books will usually only cover euclidean, affine, projective and some non-euclidean geometry. Everything else is a highly specialized field. You can't hope to cover all these topics at once.
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 15:31
$begingroup$
@Jean-ClaudeArbaut Spivak's book span about 1900 pages so a complete treatment of geometry may need some 80 000 pages, that's a scary 80 volumes of 1000 pages each. You'll need a truck to move them.
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– Euclidos
Apr 21 at 15:50
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Analysis, algebra, geometry -- you are asking 1/3 of the whole repetoire of the modern mathematics, and I am afraid it is too vast to be treated by a single book done by a single human being, and is still impossibly difficult by a series of books done by a group of people.
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– Aminopterin
Apr 21 at 18:41
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Euclid's Elements was far from comprehensive--it was an introductory textbook, even in his time.
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– Eric Wofsey
Apr 21 at 19:57