# What is the use of spherical trigonometry and the pre recs to learn it

1. Jul 3, 2014

### TitoSmooth

What is the use of spherical trigonometry besides in navigation. My math background consist of having n completed a course in calculus 1.

Would I ever need to learn and understand spherical trigonometry for further math or physics? What do I gain learning it besides saying I know spherical trigonometry.

What are good physical books that are ibtroductory or easy to read.

Thanks.

2. Jul 3, 2014

### Simon Bridge

If nothing else, it is a useful stepping-stone skill for other things - helping you handle trickier concepts and general problem solving.

There are lots of introductory physical books that are easy to read, so you can have both.
But the subject is very broad. Please be specific: what do you need from these books?
There is a whole section on PF devoted to text books BTW.

3. Jul 3, 2014

### TitoSmooth

Don't need anything in particular at the moment really. I am a math major and was wondering if learning spherical trigonometry will help me some where In my education path. Ie in physics or further math courses.

4. Jul 3, 2014

### micromass

Staff Emeritus
It's useful in navigation and astronomy. But most math majors don't need spherical trigonometry at all. Most physics majors don't need it either.

Instead of spherical trig, I recommend you to do differential geometry of curves and surfaces. That contains spherical trigonometry as a special case and it will be useful in a lot of math and physics.

5. Jul 3, 2014

### Simon Bridge

What he said.

6. Jul 4, 2014

### TitoSmooth

Thanks to both of you guys. I wrote it in my things to know rhodia notebook.

At the moment I think differential geometry would near impossible to learn. I would need maybe a yr or 2 max to began the study of it.
I have no kniwledge of mathematical proofs.

I think time bettet spent now will be learning euclidean geometry from kisselev planmetry and solid geometry from part 2.

I will gey started with the book,"How to prove it." Yo know proofs and the language of math.
I feel that by learning proofs I will spend less time trying to understand the information contained in a mathbook.

Thanks.

7. Jul 4, 2014

### mathwonk

I recommend learning spherical geometry, (not sure what spherical trig is). Last I heard the earth we live on is roughly spherical.

But I like the idea of learning special cases and proceeding to the general ones later, rather than the other way around. So I will confuse the issue for you by giving the opposite of micromass's advice.

I.e. for me it seems useful to learn the special cases of constant curvature geometry first, before general differential geometry, namely euclidean, spherical, and hyperbolic geometry.

Some really good books starting in this elementary way, and including spherical geometry, are Geometrya nd Groups, by Nikulin and Shafarevich, and some books by David Henderson, on geometrya nd differential geometry:

heres a free one:

http://projecteuclid.org/euclid.bia/1399917370

and another one I like: (I have the second edition)

http://www.biblio.com/experiencing-geometry-by-w-henderson-david/work/1588275

8. Jul 4, 2014

### SteamKing

Staff Emeritus
Spherical trigonometry is the study of three sided figures and other polygons inscribed on, naturally, a sphere:

http://en.wikipedia.org/wiki/Spherical_trigonometry

The rules of plane trigonometry are a little different than the rules in spherical trig.

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