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?
A lot.
Mathematicians like to be abstract, the Classical (Euclidean) Geometry is good but it is not sufficiently abstract enough. Thus, there are several version using its only abstraction.For example, there is axiomatic geometry, elliptical geometry, etc.
How many more level of geometry are there and what is the purpose?
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
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.
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.
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.