Three-dimensional Counterparts for Two-dimensional Objects

Date: 03/04/98 at 19:28:57
From: Amy
Subject: Points-Lines-and Planes

I need to name a 2- or 3-dimensional counterpart for a line, a polygon, 
perpendicular lines, and collinear lines. How do I do this?

Date: 03/04/98 at 19:51:47
From: Doctor Sam
Subject: Re: Points-Lines-and Planes

Amy,

Lines, polygons, perpendicular lines, and collinear lines are all 
terms that refer to things that you can draw on paper. I think you are 
asking for three-dimensional objects, or things that can exist in 
space.

All of these terms make sense in space, in our world. A telephone wire 
looks like a line, a window looks like a polygon, etc. But there are 
also three-dimensional objects that cannot be drawn on a plane, like a 
box or a pyramid or an ice-cream cone.

Now a line is a straight flat object on paper. What might "correspond" 
to that in space? How about the flat wall of a building? Or the floor 
of a room? These are examples of planes.

Just as lines can be perpendicular or parallel when drawn on paper, so 
too can planes be parallel and perpendicular. Look around you (I 
assume you are inside a room right now). The walls, floor, and 
ceiling are parts of planes. Some of these planes are parallel and 
some are perpendicular.

What about collinearity? Points that lie on the same line are called 
collinear (the word actually means "same line"). Points (and lines and 
polygons) that lie in the same plane are called coplanar ("same 
plane"). Pictures hanging on the same wall of your room are coplanar 
rectangles. Pictures that hang on different walls are not coplanar.

Finally, what corresponds to polygons? A polygon is a closed figure 
made up of straight line segments. What kinds of objects can you name 
that are solids made up of segments of planes? A box is one example. 
Can you think of other shapes? All of these are called polyhedra 
(many-faced objects).

Does that help?

-Doctor Sam, The Math Forum
Check out our web site http://mathforum.org/dr.math/