Greenwood press

PERIODIC FUNCTIONS
69

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PLANE
A plane represents any flat two-dimensional surface that has infinite length
and width. In everyday life, we use only finite versions of planes due to limited
space and material. Walls, desktops, book covers, and floors are examples of
planes. These items are made flat, because they are easier to produce and con-
venient to write on or cover. For example, a curved wall may be interesting to
look at, but expensive to create. A flat wall, on the other hand, is much easier to
wallpaper or to fix when it is damaged. 
Planes have some useful properties that give people ideas about design and
construction. For example, the intersection of two nonidentical planes, such as
the wall and ceiling, forms a line. This idea guarantees that walls and containers
made from flat surfaces can be sealed, assuming that there are no holes in them.
A saw blade cuts in a straight line, because it represents two intersecting
planes—the saw and the piece of wood.
Another property of planes is that three noncollinear points lie in the same
plane. For example, a triangle has three vertices, so it will lie on a flat surface.
Three-legged stools will never wobble, because the three ends of the legs lie on
the same plane—the floor—regardless of their length. Ideally though, the leg
lengths should be close to being the same to help support someone’s mass near
the center of the chair. Four-legged stools will sometimes wobble if one leg is
longer or shorter than the other legs, because the end of one of the legs is on a
different plane.
If a line or segment is perpendicular to a plane, then any congruent segments
with an endpoint on that plane and another endpoint at a common point on the
line or segment will be equidistant from the foot of the plane. Metal beams are
placed on a radio satellite to support its receiver as waves are reflected off the
dish. If they are created at the same length and intersect the receiver at the same
point, then they will land on the dish at the same distance from the center. This
method ensures that the beams land on the perimeter of the circle, since all points
on the circle are equidistant from its center, which is directly below the location
of the receiver. 
Inclined planes—planes that are raised at an angle—are used for a variety of
purposes. They are created for handicapped people in wheelchairs as an alterna-