First, let me apologize for my bad English, it's not my native language. Most areas of math for me aren't really an issue. I'm actually quite good at it. But there's one thing I absolutely despise and also something I'm very bad at: geometry. I was planning on studying theoretical physics, but after seeing how horrible I am at geometry, I've started to have doubts. So you could tell me, how important is geometry for someone who wants to study theoretical physics? And is it possible to improve my geometry skills by simply practicing a lot? Also, is applied physics very different from theoretical physics, when it comes to math?
Well, I can't speak for theoretical physics, but I can speak for basic physics. It does require that you possess geometric reasoning skills, especially with regard to similar triangles, angle deduction, and things like that. I never took geometry; I had to learn it the hard way in a physics class. I survived, but I also think I have an innate ability to understand things geometrically. Maybe you don't. Best thing I can tell you to do is to examine things geometrically whenever possible, even if you can do it analytically.
I don't know which type of geometry you mean, but unfortunately it does not really matter. Physics uses lots of geometry at every step of the way, and is extremely important in many disciplines of theoretical physics. Maybe there are some that do not, but areas that I am have some passing familiarity with (condensed matter, string theory) certainly utilize geometry extensively.
If you have no problems with the other areas of math, I highly doubt that you are incapable of mastering geometry. It might be harder for you, sure, but we all have things we find harder than others. Put in some extra effort, ask around about specific things you don't understand/aren't good at, and I'm sure you'll do fine.
Constructive geometry like the kind you find in Euclid probably won't be important for physics (maybe for geometrical optics?) but you will likely benefit from learning differential geometry and topology sometime in your studies.
Geometry is one of the most important areas of math you can learn for physics. Almost everything you do will rely on some kind of geometric reasoning. Like everything, practice makes perfect.
I think it's important to specify if you mean Euclidean geometry or the kind of geometry that's concerned with vector spaces, operators etc. According to me, the former is useful(for solving problems essentially) but not vital, whereas the latter is vital in Theoretical Physics. I do not know for Experimental, but I doubt that an experimentalists does not know quantum mechanics or relativity, and you can't study them without geometry... However, I really doubt that if you are good at maths you can't absolutely understand geometry. What stage of studies are you at?
Thanks for the replies. I think I mean Euclidean geometry. We don't use that name where I live. The kind of geometry I'm referring to is the kind where you have to, for example, proof that a certain shape is a rhombus and other stuff like that.
OK. That's definitely Euclidean Geometry. No worry, there's no need to be a champion in this field, I think. No one is interested in seeing if a professor of Theoretical Physics can prove a theorem of Euclidean Geometry. However, if you are so interested in Theoretical Physics and if you are good at Maths, I really think that you don't LIKE it because you have had a wrong approach, of something similar. Einstein said that if someone is not impressed by the building of Euclidean Geometry, they are not inclined to be theoretical scientists. Obviously, Einstein's ideas are not necessarily true. To my mind, if you start with a good book and you start right from the beginning, you will have a lot of fun with Euclidean Geometry. Moreover, once understood, there's nothing to remember. I also think I will study Theoretical Physics(though perhaps not one of the most popular branches), and this kind of Geometry has always been my favourite subject OF ALL when I was ay high school. Are you still at high school? I think so, as you are studying this stuff, though educational system may be very different. Where do you live, if you do not mind me asking? I do not think this geometry is studied at university in any European Country(in Maths or Physics), even though someone who does not even understand what is a triangle and its basic properties(or similar basic stuff) is surely not a strong candidate for a Physics degree! As far as the other kind of geometry we reffered to, I do not know how to specify further, but it's the kind of stuff that starts with linear algebra(indispensable for Quantum Mechanics), and then develops in tensor calculus, differential geometry and Riemannian Geometry(the language of General Relativity). It's not strongly connected to triangles, circles and squares, it's all abstract mathematical concept, but, again, try to approach Euclidean Geometry in the right way. You will have a lot of benefits from it. Remember also what Einstein said: though not necessarily true, there must be a reason why it's been handed down to us. NOTE: I am only a bachelor student in Physics, but I have tried to explain my opinion. Good luck!
Thanks iorfus. I live in the Netherlands and yes, I'm still in high school. Would you mind recommending some links and/or books to read about Euclidian geometry? You're right about the fact that I never really had a good approach to geometry.
Geometry is very important! The whole of classical mechanics is pretty much the study of symplectic geometries, classical field theory (essentially relativity) is heavily based on geometry also. If you struggle with geometry but you are okay with other areas of maths, perhaps it is because the elementary geometry you come across isn't very well derived and you just get presented with equations? The geometry that will come in handy in higher level physics isn't the geometry of Euclidean 3-Space and it is far better derived, I wouldn't worry too much about not liking geometry yet :p
I suspected about the wrong approach, and also about the fact you are in high school, because as soon as you'll get into university you will know the difference between the two kinds of geometries and you will start specifying about that like we all are doing now! I want to let you know that the wrong approach to Euclidean Geometry in high school may be due to the fact that also excellent teachers are not versed in the subject, because they have NEVER studied it at university. So, if they remember it from high school, you are lucky, otherwise... Indeed, in my high school, everyone hated Euclidean Geometry. Everyone! I started loving it and studying it because I was keen on it. As far as reference to links/books, I am Italian, I do not know anything reliable in English, let alone in Dutch, because I ONLY studied Euclidean Geometry in the FIRST and SECOND year of my completely Italian high school y(tough I refreshed my memory on the subject later, because it's really amusing, useful and develops you reasoning). I can only advise you an Italian book, and I dont think it would be useful! Ask to someone else, maybe a mentor, for a reliable book, and start having fun with this magnificent early achievement of human kind. In my view, you'll find it terribly useful, though perhaps not directly, for your future studies.
One way to try to like geometry, or at least appreciate it, is through its history: see how the subject develops through the ages; math is not a cold subject, it is a human endeavor full with interesting stories. You can try e.g. Geometry Civilized: History, Culture, and Technique.
You're welcome. Following Yenchin Suggestion, I can advise you History of Mathematics on youtube, by Marcus du Sautoy and from BBC. I do not know if there's in Dutch. There's also the BBC podcast series A Brief History of Mathematics, always by the famous Marcus du Sautoy, but there's not much about Euclidean Geometry. You can also practise your listening English skills, and this is not negative! Bye :-)
Geometry is extremely important even to just conceptualize the physics. It is of course very important for actual problem solving from trig functions to differential geometry but being able to think geometrically has its advantages (which I'm quite poor at myself).