I Walk The Line
- Mathew Purser
A line is breadthless length. A line has length but no width, it is one-dimensional. Breadth is an old way of saying width, so "breadthless" means "without width." In a more modern sense, we say that a line is an infinite collection of points. Points have no width, but if you string an infinite amount of them together in a common direction you get an infinitely long but completely thin string, a line. In fact, the word line comes from the Latin word linum, which can mean string/thread. The ends of a line are points. As straight forward as it seems, if a line ends then that end is a point. This definition doesn't differentiate between lines, line segments, and rays but we generally separate these terms today: Lines- No endpoints Rays- One endpoint Line Segments- Two endpoints Notice we haven't said that lines are "straight" as we normally would, the definition above is generally what most mathematicians would call a curve today but here we have... A straight line is a line which lies evenly with the points on itself. This definition feels strange but how would you describe "straight" to someone who can't see? Not so easy to come up with an explanation is it? When this definition says "lies evenly with the points on itself" it means that the points occur one after another with no difference in their position. Imagine lines like strings of pearls, if you let the string fall how ever it wants, you just formed a curve, if you pull the ends of the string tight you form a line.
Now we have more tools in our Geogebra toolbar, will draw a line using two points, click for the first point then click a second time for the second point to draw your line. will draw a line segment and will draw a ray with the same controls as . Play around with the tools and get comfortable using these buttons.