SOLUTION: Is a complete understanding of two-dimensional geometry necessary for an understanding of three-dimensional geometry? Why?

Question 886259: Is a complete understanding of two-dimensional geometry necessary for an understanding of three-dimensional geometry? Why?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Geometry is all about shapes and their properties. These shapes can be 0, 1, 2, or 3 dimensions. Even more dimensions are possible - consider calculus on manifolds.
Examples
--------
0 dimension is a point
1 dimension is a line
2 dimensions is a plane (we see triangles, circles, parabolas, squares, rectangles, hyperbolas, polygons, etc.)
3 dimensions is solids (we see prisms, pyramids, cubes, sphere, cylinder, etc)
In geometry understanding the shapes of a particular dimension builds on the understanding of the previous dimensions. So yes, understanding 2 dimensional geometry is required before understanding 3-D geometry.

RELATED QUESTIONS
Why is a complete understanding of two-dimensional geometry necessary for an... (answered by rfer)

Why is a complete understanding of two dimensional geometry necessary for an... (answered by rfer)

Is a complete understanding of two dimensional geometry necessary for an understanding of (answered by rfer)

Why is a complete understanding of two dimensional (answered by richwmiller)

how do you find the line of intersection of two planes in geometry, using 3 dimensional... (answered by stanbon)

Discuss in detail why the dimension of a finite dimensional vector space is... (answered by ikleyn)

Are there any interesting properties of three dimensional right triangles? Do they work... (answered by Alan3354)

determine the volume and surface of a three dimensional figure use pi for... (answered by fcabanski)

WHAT IS A THREE DIMENSIONAL OBJECT WHICH HAS ONE BASE WITH SIDES OF THE SAME LENGTH? (answered by Edwin McCravy)