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I have always been fascinated by Euclidean geometry and it was my favourite subject at school. However, I have noticed that Euclidean geometry is not very popular among pure math students (except IMO students). It seems that most people prefer not to learn more about it and it has become something like a “dead field”. It is weird that geometry is probably the oldest field of math, but I struggle to find books for geometry and I can easily find thousands of good books on calculus, analysis, topology, etc. in minutes. I have tried to find some good books on Euclidean geometry that go beyond the basic school curriculum and cover more advanced topics, such as the nine-point circle, Morley’s theorem, Ceva’s theorem, Menelaus’ theorem, Ptolemy’s theorem, etc. However (I posted questions like this here (asking for book recommendations for geometry that don't use any math other than geometry like linear algebra , group theory ,.. etc) and here (this was my first question on this site before I even knew about dup questions ) ), I have not been very successful in finding such books. Most of the books I have found are either too elementary or too old and I struggled to find any modern book about geometry that goes beyond high school. It seems that nobody wants to write a book about it anymore and that makes me think it is a dead field.

This makes me wonder why Euclidean geometry is so neglected in modern mathematics. Is it because it is not practical or useful for modern applications and technology anymore? Is it because it is an old field? Is it because it is not relevant or interesting anymore? Personally, I do not think any of these reasons are valid. I think the reason for someone to study pure mathematics is curiosity and interest not how practical and applicable math is and I think that geometry is still interesting and worth studying but I still don't understand why nobody cares about it anymore.

pie
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    There's a good book in the inexpensive Dover series by Dan Pedoe on geometry, https://www.amazon.com/Geometry-Comprehensive-Course-Dover-Mathematics/dp/0486658120 – coffeemath Oct 13 '23 at 20:01
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    An interesting book bridging classical and modern geometry : "Plane Geometry and its groups" (Heinrich Guggenheimer), Holden Day editor : https://www.amazon.com/Plane-geometry-groups-Holden-Day-mathematics/dp/B0007DO7VI – Jean Marie Oct 13 '23 at 22:07
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    See also "Geometry Revisited" by Coxeter (famous mathematician) and Greitzer : https://www.amazon.fr/Geometry-Revisited-H-S-Coxeter/dp/0883856190 – Jean Marie Oct 13 '23 at 22:09
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    Similar question here. – Jean Marie Oct 13 '23 at 22:11
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    @JeanMarie it is my own question and I didn't got good enough answers even after the bounty – pie Oct 14 '23 at 07:48
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    A liitle remark : you should mention in your new question the old one : it would avoid people to spend time for finaly finding the past question without noticing it comes from the very same person... – Jean Marie Oct 14 '23 at 09:01
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    Another similar question : https://math.stackexchange.com/q/3799333/305862 – Jean Marie Oct 14 '23 at 09:03
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    I want to echo support for Pedoe's wonderful book and for Berger's Geometry I and II. Both are superbly written and cover Euclidean geometry and a lot, lot more. These are far beyond "high school geometry" level. – Ted Shifrin Oct 14 '23 at 18:00
  • If you know Portuguese, there is a really good series of books called 'Tópicos de Matemática Elementar' by Antonio Caminha. The second volume of this series covers Euclidean geometry, including the theorems you mentioned and many more. – SilverBladeII Oct 14 '23 at 18:52

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Euclidean geometry is taught to every high-school student in America. University courses preparing students for research careers focus on the fields where major unsolved problems exist (Riemann hypothesis, twin-prime conjecture, Collatz conjecture, ...). There simply are not many of the elite profound unsolved problems in Euclidean geometry that exist in other areas of math (number theory, topology, analysis, ...).

That is why.