Euclidean geometry: main theorems, formulas and concepts

[greg_rack]

Hi guys,

Hopefully, no geometry-enthusiasts are going to read these next few lines, but if that's the case, be lenient :)

I have always hated high-school geometry, those basic boring theorems about triangles, polygons, circles, and so on, and I have always "skipped" such classes, studying everything the day before the test, just to get a decent mark.
But unfortunately, as I dive into more advanced mathematical and engineering concepts it keeps getting clearer to me that I should have a much deeper mastery of those "basic boring theorems", being confident with handling such "geometrical situations".

That is basically the reason for which I'm writing this post: to ask you if, and if yes, where I could find an exhaustive and complete "recap" of all the notions every engineer(or physicist) should master to solve much more complex problems... and take advantage of it to delve a bit deeper into my "dark side of mathematics".

Thanks in advance for any response,
and forgive me for this shameless declaration of ignorance

 

[Vanadium 50]

What is it you want exactly? A geometry book that is not a geometry book? Just mensuration formulas? Something else?

 

[greg_rack]

What is it you want exactly? A geometry book that is not a geometry book? Just mensuration formulas? Something else?

I'm not sure it's possible with no effort(e.g. without buying a proper textbook), but it'd be perfect to have a geometry "pantry" with all the fundamental properties of triangles, main theorems, the most useful formulas to solve applied geometry problems... without spending much time in literally studying all derivations and "history" in order, such as a textbook would.

Hope it's clearer now, but I'm not sure it makes any sense

 

[fresh_42]

Sounds to me like:
https://en.wikipedia.org/wiki/List_of_trigonometric_identities
https://de.wikipedia.org/wiki/Formelsammlung_Geometrie
(no english version, I recommend Google Chrome for translation)
https://de.wikipedia.org/wiki/Formelsammlung_analytische_Geometrie
(english version is ridiculously thin, same procedure as above recommended)
Also consider the links.

Another approach is:
Search for 'geometry + formulas', 'geometry of triangles', 'Platonic solids', 'analytical geometry', or simply download https://openstax.org/details/books/algebra-and-trigonometry

 

[Vanadium 50]

The best HS textbook is Geometry for Enjoyment and Challenge, by Rhoad, Milauskas and Whipple. I cannot say with certainty, however, that it does not contain a sliver of unwanted information. Also, what makes it the best is the problems. That may not interest you.

On the other extreme are the four page "noah sheets" (attached).

If you are primarily interested in mensuration formulas, the CRC Handbook of Standard Mathematical Tables (not the Handbook of Chemistry and Physics!) is my go-to book. I consider it having reached its peak in the late 1980's, after having introduced linear algebra into much of the geometry.

If none of these do it for you, I fear that what you want may not exactly exist.

 

[greg_rack]

If you are primarily interested in mensuration formulas, the CRC Handbook of Standard Mathematical Tables (not the Handbook of Chemistry and Physics!) is my go-to book. I consider it having reached its peak in the late 1980's, after having introduced linear algebra into much of the geometry.

That definitely caught my interest!

After some research, however, I found out that this( ) is the only edition available for shipment to Italy... and it costs nearly 100€, which looks a lot to me.
What do you think? Would it be worth it, or should I look for other such handbooks?

 

[fresh_42]

I bet there are quite a few Italian books which cover the formulas you are looking for! Too bad that Spanish and Italian is indistinguishable when searching for 'geometria' and 'formula', but I guess the other terms are so closely related, that it doesn't matter. And this is a good starting point, or this.

On the first page of a Google search (geometria formule pdf)
https://www.caramuelroncalli.it/wp/wp-content/uploads/2016/10/Geometria-piana-e-solida_Casalena.pdf
http://www.liceoartisticoteramo.it/bes/formulario_geometria.pdf

 

[greg_rack]

I bet there are quite a few Italian books which cover the formulas you are looking for! Too bad that Spanish and Italian is indistinguishable when searching for 'geometria' and 'formula', but I guess the other terms are so closely related, that it doesn't matter. And this is a good starting point, or this.

On the first page of a Google search (geometria formule pdf)
https://www.caramuelroncalli.it/wp/wp-content/uploads/2016/10/Geometria-piana-e-solida_Casalena.pdf
http://www.liceoartisticoteramo.it/bes/formulario_geometria.pdf

Having switched my browser language to English, I experienced how much of a pain is researching stuff in Italian... results are given in Portuguese or Spanish most of the time! :)

Anyway, since next year I'll study engineering abroad, I was interested in having such a book in the English version, just to start getting familiar with the language from a scientific point of view.

 

[fresh_42]

Anyway, since next year I'll study engineering abroad, I was interested in having such a book in the English version, just to start getting familiar with the language from a scientific point of view.

A tip how to translate technical terms into English, or find them. I often look up the German [Italian] Wikipedia page and then switch - if it exists - to the English version. This is far better than a dictionary when it comes to technical terms. Also Google translate in Chrome is not so bad. The English version isn't always the best or most detailed one. You can easily switch to another Roman language and see if it is a better version. E.g. I regularly look up the French site if I want to know how L'Hôpital is really written!

 

[Vanadium 50]

I wouldn't spend 100 EUR on it. I'd wait for a cheaper used one to become available. After all, you've waited this long.

 

[atyy]

I liked John Roe's Elementary Geometry.
https://books.google.com.sg/books?id=Xmb44wyy7gEC&source=gbs_navlinks_s

 

[Delta2]

Just learn law of cosines and law of sines. But you also need to know a bit of trigonometric identities about sines and cosines. With the above you can deal with 70-80% of the problems in engineering/physics.
Law of cosines - Wikipedia
Law of sines - Wikipedia
List of trigonometric identities - Wikipedia

But of course you also need to know some basic geometry (such as that angles from two intersecting lines that share the same vertex are equal, or that the sum of angles of a triangle equals 180degrees).

 

[greg_rack]

Thanks y'all, guys!

I'll treasure your suggestions

 

[vanhees71]

Hm, at this stage of education, I'd suggest to learn Euclidean geometry from the very beginning using vectors (linear algebra). It's simpler to learn than drawing a lot by ruler and compass as in middle school (when I hated the subject too ;-)) and it's what you need to learn in physics and engineering anyway.

 

[greg_rack]

Hm, at this stage of education, I'd suggest to learn Euclidean geometry from the very beginning using vectors (linear algebra). It's simpler to learn than drawing a lot by ruler and compass as in middle school (when I hated the subject too ;-)) and it's what you need to learn in physics and engineering anyway.

I am relieved to not be the only one hating secondary school geometry :)

Definitely going to give linear algebra a chance before university... it has always caught my interest!