Can someone explain how many different types of geometry courses there are?

For example, there is axiomatic geometry, elliptical geometry, etc.

How many more level of geometry are there and what is the purpose?

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- Jan 11th 2007, 04:48 PMsymmetryGeometry
Can someone explain how many different types of geometry courses there are?

For example, there is axiomatic geometry, elliptical geometry, etc.

How many more level of geometry are there and what is the purpose? - Jan 11th 2007, 05:40 PMThePerfectHacker
A lot.

Quote:

For example, there is axiomatic geometry, elliptical geometry, etc.

How many more level of geometry are there and what is the purpose?

- Jan 12th 2007, 02:35 AMsymmetryok
So, basically geometry is almost endless. I like working with geometric shapes. I find triangles, rectangles, etc so interesting, fun to draw and play with in the math world.

- Jan 12th 2007, 04:31 AMCaptainBlack
I'm not sure that there is a progression of geometry courses. But the

main forms of geometry that you will come accross are:

Synthetic Geometry (euclidean)

Non-Euclidian Geomentry (hyberbolic and elliptic)

Remannian

Cartesian Geometry (coordinate geomentry)

Projective Geometry

Differential Geometry

Algebraic Geomentry

:

:

You will find a whole bag more in the Wikipedia article on geometry here

RonL

RonL - Jan 12th 2007, 06:51 AMThePerfectHacker
- Jan 12th 2007, 07:49 AMCaptainBlack
- Jan 12th 2007, 01:39 PMQuick
Just a side thought, is trigonometry part of geometry, or is it a different subject?

- Jan 12th 2007, 04:13 PMsymmetryok
I took trigonometry back in high school over 20 years ago. I recall trig using geometric shapes in many questions, especially in terms of angles of elevation and depression and right triangle trigonometry.

symmetry - Jan 12th 2007, 04:20 PMAfterShock
- Jan 13th 2007, 02:21 PMThePerfectHacker
I would say it is its own subject.

The most basic part of trignometry is part of geometry. But it gets more involved than that. For example you can find sines and cosines for angles larger than 90 degree (even though geometrically it is undefined). And for negative angles. And then you learn about sine and cosine functions. Thus, it is completely distinct from geometry, though it has some applications to geometry. - Jan 14th 2007, 04:25 AMsymmetryok
Trigonometry is not math?

Trigonometry easy?

Maybe high school trigonometry is easy but there are aspects of trigonometry that are simply to complicated for most people.

Take for example, the trig used in astronomy math science. I have never seen anything more complicated than astronomy mathematical concepts. - Jan 14th 2007, 07:30 AMThePerfectHacker
I think there are much more complicated things. The worse trigonomtry gets in applied math is when you need to rotate something in 3-dimensions.*

*)But there are some still complicated things. A famous story with Gauss:

Some astronomers found a comet called "Ceres" and soon were unable to find it. They called Gauss, who was known to be an excellent mathematician. They shown him all the infromation they had with the comet, its speed, its last locations, its altitute,.... Gauss correctly solved the problem and the team of astronomers were able to find the comet. But the amazing thing about what Gauss did is that he worked, by hand, with about 80 variables. Furthermore, was able to deduce the location of the comet was very very little infromation.