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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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.Quote:
Originally Posted by symmetry
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.Quote:
For example, there is axiomatic geometry, elliptical geometry, etc.
How many more level of geometry are there and what is the purpose?
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.
I'm not sure that there is a progression of geometry courses. But theQuote:
Originally Posted by symmetry
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
That is not a geometry related. At least I think.Quote:
Originally Posted by CaptainBlack
It still needs including as it calls itself geomentry.Quote:
Originally Posted by ThePerfectHacker
But of course some varieties of Topology should also be on the list
RonL
Just a side thought, is trigonometry part of geometry, or is it a different subject?
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
Trig is a whole new subject. However, a lot of geometry uses trig, especially in higher non-euclidean geometry where some of the Euclidean rules apply (in some instances in certain manifolds, the hyperbolic plane, and so forth).Quote:
Originally Posted by Quick
I would say it is its own subject.Quote:
Originally Posted by Quick
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.*Quote:
Originally Posted by symmetry
*)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.