different branches of Geometry?

Answer 1

Euclidean and non-Euclidean. Differential geometry. There are geometries of virtually anything: multidimensional spaces, spheres, populations, topological objects, surfaces, manifolds, probability spaces. Just about anything that can be conceived in other branches of mathematics can be given a geometrical interpretation.

Answer 2

Branches Of Geometry

Answer 3

This can cover a lot of ground. There's geometry that be based on a limited number of points (such as 3-point, 4-point, and 5-point geometry).

In terms of plane geometry, there's Euclidian geometry, that takes Euclid's fifth postulate to be true. Then there's hyperbolic geometry, which doesn't. Going against Hilbert's postulates, there's elliptic geometry as well. The differences of the three is that Euclidian geometry states that triangle angles add up to 180 degrees, hyperbolic says it's less than that, elliptic says that it's more than that.

Then there's the whole issue of 3-D, 4-D, 5-D, etc., geometries, worked out in multi-dimensional spaces. Scientists that work with relativity use a specialised Minkowski geometry to explain space-time.

Then there's the analytical application of all of the above, which can lead to the related branch of trigonometry. And I speculate that there are a bunch of other specialised geometries that I'm not yet aware of.

Hope that helps.

Answer 4

depends on what you mean by "branches." I take it to mean fields of study within geometry. If so then two main branches come forth:

Euclidean and Non-Euclidean

Euclidean is the geometry you study in school. All the things they have you prove about parallel lines, perpendicular lines, tangents, circles, etc. These proofs rely upon certain truths or axioms which may not apply in non-Euclidean geometry.

non-Euclidean is generally thought of in relation to space and Einsteins theory of relativity. The difference requires a bit of understanding of each of the divisions to go fully in depth.

There are several sub-divisions/branches you can divide geometry even within these two major branches. Modern times have found even newer geometry's like numerical geometry and geometric algorithms.

The many branches and their uses can be found here:

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

Enjoy!

Answer 5

There are THREE different kinds of "plane" (flat) geometry: they all hinge on Euclid's "fifth postulate": that given one line and one point, there is exactly one other line that goes through that point parallel to the first line. Mathematicians since Euclid note that the fifth postulate should NOT be assumed true (as Euclid himself assumed) -- there is insufficient reason to believe it self-evident. So there are TWO alternative "non-Euclidian" geometries: Lobochevskian and Reimannian. In Lobochevskian geometry, the fifth postulate says that there are an INFINITE number of lines through a point parallel to the first line, and in Reimannian geometry the fifth postulate says that there are ZERO lines through a point parallel to the first. The consequences of how you state the fifth postulate are great: for example the measure of the three angles of a triangle sum to 180 degress in Euclid, always more than 180 degrees in Lobochevski, and always less than 180 degrees in Reimann. Euclidian space is a flat surface, Lobochevskian space can be modelled as a sphere (lines of longitude are "parallel" and the poles are points through which they pass) and Reimann space looks like the centre of an old-fashioned washing machine (a sort of distorted cone). All three are valid and serve useful purposes in calculations (especially in relation to trigonometry and calculus) .

Answer 6

Branches of Geometry:

1. Plane Geometry >> deals with lines, planes, areas,
geometric shapes such as square,
triangles, rhombus, parallelograms,etc.
However, in dealing with triangles, we
have trigonometry, which deals with t
sides and angles of triangles.

2. Solid geometry >> deals with volumes such as cylinders,
cones, cubes, etc.

3. Analytic Geometry > deals with analyses of planes and solids,
such as the X-Y graphs, parabolas,
hyperbolas, matrixes, etc.

But of course, after these courses, we have the calculus,
which deals with limits, instantaneous rates of change and finding areas and volumes.

Answer 7

Euclidean and non-Euclidean.
Euclidean leads to pur geometry deals with theorems and riders.
non-Euclidean deals with analyical co-ordinate geometry. Here we have Cartisian-coordinate system in 2dimensional (x and y)
Polar coordinates, elliptical, circular (all in 2dimensional).

we have 3dimensional for Cartisian (x,yz), elliptical, circular coordinates

Hilberts hyperspace deals with x, y, z, and time

Answer 8

2-dim geometry, 3-dim, 4-dim g'y.
metric problems (area, volume)
shapes, enlarging
congruency
graph's

Answer 9

Hay! Ima mathametics prefesor and I spell pie good.