User:Boris Tsirelson/Sandbox1: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Boris Tsirelson
No edit summary
imported>Boris Tsirelson
No edit summary
Line 1: Line 1:
In Euclidean geometry, a line is a straight curve. When geometry is used to model the real world, lines are used to represent straight objects with negligible width and height. Lines are an idealisation of such objects and have no width or height at all and are usually considered to be infinitely long. Lines are a fundamental concept in some approaches to geometry such as Euclid's, but in others such as analytic geometry and Tarski's axioms they enter as derived notions defined in terms of more fundamental primitives such as points.
In Euclidean geometry, a line (sometimes called a straight line) is a straight curve having no thickness and extending infinitely in both directions. Line, together with point, is a basic concept of elementary geometry. It is the shortest way between two points.
 
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line (Casey 1893), to emphasize that it has no "wiggles" anywhere along its length. While lines are intrinsically one-dimensional objects, they may be embedded in higher dimensional spaces.
 
Line (actually a straight line), together with point, is a basic concept of elementary geometry. The idea of line is an abstraction that distills our intuition that a straight line is the shortest way between two points. However, we distinguish between a line and a line segment. A line segment includes the endpoints, i.e. the points that it joins. The line through the two points continues beyond these points indefinitely.
 
A line is one of the basic terms in geometry. We may think of a line as a "straight" line that we might draw with a ruler on a piece of paper, except that in geometry, a line extends forever in both directions.
 
 
In geometry a line: is straight (no curves), has no thickness, and extends in both directions without end (infinitely).

Revision as of 10:36, 12 May 2010

In Euclidean geometry, a line (sometimes called a straight line) is a straight curve having no thickness and extending infinitely in both directions. Line, together with point, is a basic concept of elementary geometry. It is the shortest way between two points.

Retrieved from "https://citizendium.org/wiki/index.php?title=User:Boris_Tsirelson/Sandbox1&oldid=628566"