Drawing the Line

Geometry: Part 1
Drawing the Line

We saw the "line" earlier, when we put numbers on it. I was working on an assumption that I knew what a line was.  But this is a blog about what I know, and I have laid down numbers about as far as I can go, so I will be moving on to geometry, the science of construction.

On a flat surface, the straight line is the shortest distance between to places.  On the surface of a sphere, that line is necessarily curved in relation to the radius of that sphere. I will begin with flat surfaces and straight lines in what is called "plane geometry."  That is not "plain," but "plane," as in flat.  It is what we usually think of when building things anyway.

I should begin with the zeroth dimension, which is the point.  A point has no dimensions, but it has coordinates.  The best way to envision a point, though, is as a very small circle, just big enough to see.  That way, we will know where we are and can see where we are going.

To make this practical, as a Greek guy named Euclid did, we will envision laying out a patio.  Making the sides straight will not be hard, and the next blog I will deal with making it rectangular -- or at least triangular, which is exactly half of a rectangle.  But first, the line.

It is quite easy to draw a straight line.  With nothing but a few pegs, a mallet and a measured cord, a perfectly straight line will be a cinch.  After placing a peg in the first corner, measure out a length of cord to a multiple of 4 that is equal to, or beyond the length of the patio.  Do not cut the cord, for you will need twice that much more to assure a square corner.

* * * three pegs
and a cord
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But first, the straight line must be drawn.  With one end secured to the first peg, pull the cord taunt. With a second peg connected to the end of the cord, etch an arch of maybe step in each direction, tentatively marking the middle of that arch.

If the cord is tight, you have your first straight line.  It is the shortest distances between the chosen points.  The slight curved line that you have made in the sand is the beginning of a big circle with a radius the length of that line, but that will come in handy later.

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So, what do I know?

A straight line on a plane is the shortest distance between two points.  The easiest way to make a straight line is with a string, cord or rope.  Even with modern tools, this is sometimes faster.

A point in space has no dimensions, and a line is in one dimension on flat surface in two opposite directions.

Next: A right triangle.