Curve: Difference between revisions
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== Line == | == Line == | ||
A '''line''' is a straight | A '''line''' is a straight curve, which is long enough that its boundaries can be ignored. Straightness is a property that can be recognized perceptually, and also through [[Riemannian geometry|more sophisticated means]]. | ||
Lines are one of the central concepts of [[classical geometry]]. | 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. | 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. | |||
== See also == | == See also == | ||
Revision as of 04:50, 14 February 2024
A curve is an entity of nill breadth and depth.[1]
Line
A line is a straight curve, which is long enough that its boundaries can be ignored. Straightness is a property that can be recognized 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.
See also
References
- ↑ I got the idea for this definition from HB https://www.youtube.com/watch?v=GwHAObb7tt8&t=1301s