Points and lines
What is this • ?
You probably said, “It’s a dot.” Or maybe you said, “It’s a period.”
Well, it could be a dot or a period. But to mathematicians, it’s a
picture of a point.
You probably think of a point as the sharp tip of a needle or a pin. But
to mathematicians, a point is a place. When you say to a friend, “I’ll
see you down at the corner,” you mean a place where two streets meet. A
mathematician might talk about a place by saying, “It is at the
point where the two lines cross.”
If you look at the point where the two lines cross, you won’t see
anything. That’s because a point is invisible. It’s just an idea. A
point has no length, or width, or thickness. Because we can’t measure a
point, we say that a point has no dimensions. But to show where a point
is, we often put a dot there. So the picture of a point does have some
size and shape.
You can’t see or measure a point. But when you have a lot of these
invisible points in a row, all touching each other, they make something
that you can see and measure. They make a line! At least that’s the way
mathematicians think of a line—as a row of points.
Now, a line has length, doesn’t it? You can measure the length of a line
with a ruler. So a line has one dimension, length. Mathematicians think
of a line as having no width or thickness. Of course, we can’t draw it
this way. Even the finest line you can draw has some width.
None of this seems very important, does it? But it is! You see, every
line is made up of a great many points. And every shape—triangles,
squares, circles—is made up of lines. So, points and lines are the
things we use to make designs. Without them, we couldn’t make any
designs.
