1. ## World of Geometries

I searched online for different geometries. The website makes known the fact that the more common geometry taught in elementary school through high school is called Euclidean Geometry but there are also non-Euclidean Geometries.

Although I am not be there mathematically or may never be in terms of learning, can someone define in simple terms the following geometries?

*Spherical Geometry
*Differential Geometry
*Axiomatic Geometry

What about geometry that deals with crop circles? What level of artistic geometry is this in all its form?

2. ## Re: World of Geometries

"Spherical geometry" is the geometry you get if you take "point" to be a point on the surface of a given sphere, "line" to be a great circle on that sphere. Spherical geometries have the property that all lines intersect- there are no "parallel" lines. "Differential geometry" can be the geometry on any surface- the important thing is that we be able to use Calculus to fid such things a tangent lines or planes to the surface. "Axiomatic Geometry" is any form of geometry in which we are given "axioms" that are used to prove theorems in the geometry.

I have no idea why you would think there would be a particular geometry for "crop circles"! Since crop circles occur on portions of the surface of the earth, small enough that the curvature of the earth, "Euclidean Geometry" would be appropriate. And I do not know what you mean by "artistic geometry".

3. ## Re: World of Geometries

Originally Posted by HallsofIvy
"Spherical geometry" is the geometry you get if you take "point" to be a point on the surface of a given sphere, "line" to be a great circle on that sphere. Spherical geometries have the property that all lines intersect- there are no "parallel" lines. "Differential geometry" can be the geometry on any surface- the important thing is that we be able to use Calculus to fid such things a tangent lines or planes to the surface. "Axiomatic Geometry" is any form of geometry in which we are given "axioms" that are used to prove theorems in the geometry.

I have no idea why you would think there would be a particular geometry for "crop circles"! Since crop circles occur on portions of the surface of the earth, small enough that the curvature of the earth, "Euclidean Geometry" would be appropriate. And I do not know what you mean by "artistic geometry".
Check out this link. I define crop circle geometry as ARTISTIC GEOMETRY because of the beautiful art display that it is famous for in the world of geometry.

Cool math Lessons - The Geometry of Crop Circles