1

I am currently a high school student interested in a research career in physics. I have self taught myself single variable calculus and elementary physics upto the level of IPHO . And I am comfortable with euclidean geometry upto the point of some basic theorems like Pythagoras or Thales and the geometry in Cartesian coordinates and use of vectors.

I have read at a lot of places that somehow geometry is very much essential for doing physics? Now I don't know in what context, as in do you ever need the complex geometrical theorems that are upto the level of IMO, in physics or are you just good knowing simple theorems and their proofs and trigonometric relations and similarity etc.

Plus what other forms of geometry are essential for doing physics?

Is linear algebra a form of geometry?

What next step should I take to dive into geometry that will help me in my physics career for making an early start? Non-euclidean? And what is it about the geometry names, hyperbolic, elliptical? I can understand if someone tells me that plane geometry / 3d geometry, but what is the essence of hyperbolic/elliptical geometry?

And what are non euclidean geometries and topologies?

Is there a theoretical minimum that you need in all forms of geometries to do physics? I want to learn the math now properly so that I get used to its machinery and later on, don't have to struggle with it later, especially geometry, since the names of these geometries intrigue me .

Is there any need for learning euclidean geometry, upto the levels of Geometry Revisited by Coxeter?

Also I'd be grateful, if some book recommendations are also provided.

Andrew Tom
  • 41
  • 2
    Hi Andrew. Welcome to Physics.SE. First, Please have a look on both the tag definitions. And, please don't ask too many questions on a single post. You can ask them as a new questions ;-) – Waffle's Crazy Peanut Apr 20 '13 at 17:03
  • 1
    That's a whole lot of questions, many of which are rather open-ended. Just a short response: (1) Contest-style physics (or math) is quite unrelated to research; you'll know if you really like research-style once you're taking advanced classes in college. (2) The geometry required by all physics is basic trig - nothing more fancy or complicated. (3) Certain branches of physics (GR, strings) use more advanced "geometry," but this is something entirely different (differential or algebraic), and knowing more Euclidean geometry won't necessarily help with these. –  Apr 20 '13 at 17:08
  • @ChrisWhite So , what should I do next in learning geometry ? – Andrew Tom Apr 20 '13 at 17:13
  • Possible duplicates: http://physics.stackexchange.com/q/234/2451 and links therein. – Qmechanic Apr 20 '13 at 17:15
  • @AndrewTom You're going to need a broader background for the more advanced stuff. Linear algebra is a must for attempting differential geometry, and besides lin. alg. is a must for basically all of physics anyway. Take a step to the side before attempting another step forward. –  Apr 20 '13 at 17:18
  • @ChrisWhite Any good mathematical physics textbook , that fulfils the requirement for a beginner in learning linear algebra, differential geometry and other mathematics needed for doing physics ? – Andrew Tom Apr 20 '13 at 17:40
  • Hi Andrew Tom. We only allow a few well-posed soft-questions asking for prerequisites and book-recommendation. Your question(v1) is also too broad, so I'm closing it. (I'm technically closing it as a duplicate, but the real reasons are given above.) – Qmechanic Apr 20 '13 at 17:59
  • @AndrewTom edit you question according to the forum rules, In any case, The reason geometry is essential in physics is because we work with all kinds of geometric objects such as curved space times, and strings(more generally surfaces embedded in space time). While in most daily experiences euclidean geometry(flat space) is sufficient, in more extreme circumstances to describe new experiences(such as the apparent bending of light or physics near a massive object) we need to use a more general geometric ideas dealing with physics on curved objects, and space times. – Prathyush Apr 20 '13 at 18:55
  • I would recommend learning form a physics text book over a mathematics text book, There are a lot of excellent books which I am sure you will find. Personally I think a good place to start will be einstein's paper on the electrodynamics of moving bodies. – Prathyush Apr 20 '13 at 19:02
  • but it'll be too localised that paper , isn't it ? – Andrew Tom Apr 20 '13 at 19:16

0 Answers0