A number line is infinite in both directions – definition of a line
A line of points
A line is made of an infinite number of points that are right next to each other. So a line goes on forever in both directions. In geometry, a line is always straight, so that if you know two points on a line, then you know where that line goes. As they say, two points is the definition of a line.
What is a point?
What are whole numbers?
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How thick is a line?
A line is only one point thick (which is to say that it has no thickness, because a point has no thickness). When we mark off certain points on a line, we can use that line as a number line. When we draw a line with a pencil, we make it thick enough to see. But a line in geometry is not thick enough to see, because it is only one point thick. If you looked at a line from the end, it would look just like a point – so it would be invisible.
Perpendicular lines
Moving a line through space
If you took a line and moved it through space, like sliding a flat ruler across a table, it would create a flat plane. You can create half a line by choosing one point on a line and naming the section of line that goes on from that point.
What is a plane?
Line segments and geometry
You can also create line segments of any length by choosing two points on a line and naming the section between those two points. We use line segments for many things in geometry: one side of a triangle or a square is a line segment.
What is a triangle?
Or a square?
Parallel, perpendicular, and skew
Two lines can be parallel to each other, or they can be perpendicular. If two lines are neither parallel nor perpendicular, and they also can’t touch each other at any point, no matter how long they extend outward, then they are skew.
Parallel lines
Perpendicular lines
Skew lines
Who thought up this stuff?
Mathematicians have been working with shapes since the early Bronze Age, when they started to write things down, and maybe before that. But most of the work on the definition of a line was done by Euclid, at the University of Alexandria in Egypt, in Africa. Euclid lived in the 300s BC, about 2300 years ago. We don’t know anything much more about him than that.
