Difference between Plain & Solid Geometry

[WannabeG133]

I know this is probably the stupidest question asked, and you can flame me all you want for it, but what is the difference between Plain & Solid Geometry, Differential Geometry, and any others there might be? I'm a freshman in high school and we switch classes soon and I've got PS Geometry next term and just wondered what the differences were. Thanks for helping the uninformed stupid kid out.

 

[selfAdjoint]

Plane geometry is resricted to a plane, that is, a flat surface. So the things you study asre flat shapes: triangle, circles, parallel lines, and so on. The angles at the base of an isoceles triangle are equal.

Solid geometry happens in three dimensional space, so the objects are cubes and parallelopipeds (i.e rectangular boxes of various shapes), spheres, cones, and lines in three space (two lines determine a plane, unless they're parallel).

One you didn't mention is Analytical Geometry, which is usually taught in the US these days in a combined class called precalculus. It is about how to set up coordinates and equations to describe curves and surfaces. The unit circle is described by $$x^2 + y^2 = 1$$.

Differential geometry uses ideas derived from calculus and linear algebra to study irregularly curving objects in abstract spaces of any number of dimensions. Unlike the previous two, these higher dimensional things can't really be visualized, so the work is done mostly with equations.

 

[M98Ranger]

First of all, there is no such thing as a stupid question. It is always better to ask and seek knowledge than to remain uninformed.

Plain geometry, also known as Euclidean geometry, deals with shapes and figures that can be drawn on a flat surface, such as a piece of paper. It includes concepts such as points, lines, angles, and polygons. This type of geometry is the foundation of most high school geometry courses.

On the other hand, solid geometry, also known as three-dimensional geometry, deals with shapes and figures that exist in three-dimensional space. This includes objects such as cubes, spheres, and cones. Solid geometry is more advanced than plain geometry and is typically taught in higher level math courses.

Differential geometry is a branch of mathematics that deals with the study of curves and surfaces in three-dimensional space. It involves the use of calculus and advanced algebra to analyze and understand the properties of these curves and surfaces. Differential geometry is often used in fields such as physics and engineering.

There are many other branches of geometry, such as projective geometry, non-Euclidean geometry, and topology. Each of these branches focuses on different types of geometric concepts and may have applications in various fields.

In summary, plain geometry deals with 2D shapes, solid geometry deals with 3D shapes, and differential geometry deals with curves and surfaces in 3D space. These are just a few of the many branches of geometry, each with their own unique concepts and applications. I hope this helps clarify the differences for you. Good luck in your geometry class!