# Difference between Plain & Solid Geometry

1. Jan 10, 2004

### 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.

2. Jan 10, 2004

Staff Emeritus
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.

Last edited: Jan 10, 2004