Curve

A curve is an entity of nill breadth and depth.

Line

A line is a straight curve, which is long enough that its boundaries can be ignored. Straightness is a property that can be measured perceptually, and also through more sophisticated means.

Lines are one of the central concepts of classical geometry.

Unlike standard mathematics, the concept of a line in Objective Mathematics refers to real things, and real things have finite thicknesses and are never "completely" straight. (I don't think the idea of "completely" straight even makes sense. I am using the term in the negative, to inform the reader that this faulty concept of standard mathematics doesn't apply.) Furthermore, lines don't actually go on forever; like everything else, they are limited in size.

Examples

If I put my eye really close to the table, the edge of the piece of paper there is a line.

Non-examples

A pencil viewed from a few meters away is not a line. It is a straight curve, but its length is not long enough that its boundaries can be ignored (in most contexts. I guess.) It is a segment.

When viewed on Google Maps, the road near my house is not a line. It is an unbounded curve, but it is not straight.

Applications of rational curves

They are useful in some engineering applications. This video https://www.youtube.com/watch?v=jG4DYZ5uuE0 gives a few examples.

See also

• Point
• Surface
• Entity