Share on Facebook Share on Twitter Email
Answers.com

straight-line

 
Dictionary: straight-line   (strāt'līn')
adj.
  1. Lying in a straight line.
  2. Relating to a device whose linkage produces or copies motion in straight lines.
  3. Accounting. Of or being a mode of amortization by equal payments at stated intervals over a given period of time.

Search unanswered questions...
Enter a question here...
Search: All sources Community Q&A Reference topics
Real Estate Dictionary: Straight-Line
Top

To project a uniform level of Rent or Revenue over the life of a Lease or Contract, even when growth in that income stream is expected. Example: To create a conservative projection of investment return, the analyst straight-lined the revenue produced by concession sales and other non-rent sources.

WordNet: straight line
Top
Note: click on a word meaning below to see its connections and related words.

The noun has one meaning:

Meaning #1: a line traced by a point traveling in a constant direction; a line of zero curvature
  Antonym: curve (meaning #1)


Wikipedia: Line (geometry)
Top
A representation of one line segment
Three lines — the red and blue lines have the same slope, while the red and green ones have same y-intercept.

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.

A line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its end points. Depending on how the line segment is defined, either of the two end points may or may not be part of the line segment. Two or more line segments may have some of the same relationships as lines, such as being parallel, intersecting, or skew.

Contents

Euclidean geometry

When geometry was first formalised by Euclid in Elements, he defined lines to be "breadthless length" with a straight line being a line "which lies evenly with the points on itself".[1] These definitions serve little purpose since they use terms which are not, themselves, defined. In fact, Euclid did not use these definitions in work and probably included them just to make it clear to the reader what was being discussed. In modern geometry, a line is simply taken as an undefined object with properties given by postulates.[2]

In an axiomatic formulation of Euclidean geometry, such as that of Hilbert (Euclid's original axioms contained various flaws which have been corrected by modern mathematicians),[3] a line is stated to have certain properties which relate it to other lines and points. For example, for any two distinct points, there is a unique line containing them, and any two distinct lines intersect at most one point.[4] In two dimensions, ie. the Euclidean plane, two lines which do not intersect are called parallel. In higher dimensions, two lines that do not intersect may be parallel if they are contained in a plane, or skew if they are not.

Any collection of lines partitions the plane into convex polygons; this partition is known as an arrangement of lines.

Ray

If concept of "order" of points of a line is defined, a ray, or half-line, may be defined as well. A ray is part of a line which is finite in one direction, but infinite in the other. It can be defined by two points, the initial point, A, and one other, B. The ray is all the points in the line segment between A and B together with all points, C, on the line through A and B such that the points appear on the line in the order A, B, C.[5]

Ray

In topology, a ray in a space X is a continuous embedding R+X. It is used to define the important concept of end of the space.

Coordinate geometry

In coordinate geometry, lines in a Cartesian plane can be described algebraically by linear equations and linear functions. In two dimensions, the characteristic equation is often given by the slope-intercept form:

 y = mx + b \,

where:

m is the slope of the line.
b is the y-intercept of the line.
x is the independent variable of the function y.

In three dimensions, a line is described by parametric equations:

 x = x_0 + at \,
 y = y_0 + bt \,
 z = z_0 + ct \,

where:

x, y, and z are all functions of the independent variable t.
x0, y0, and z0 are the initial values of each respective variable.
a, b, and c are related to the slope of the line, such that the vector (a, b, c) is a parallel to the line.

In R2, every line L is described by a linear equation of the form

L=\{(x,y)\mid ax+by=c\} \,

with fixed real coefficients a, b and c such that a and b are not both zero (see Linear equation for other forms). Important properties of these lines are their slope, x-intercept and y-intercept. The eccentricity of a straight line is infinity.

Euclidean space

In Euclidean space Rn (and analogously in all other vector spaces), we define a line L as a subset of the form

L = \{\mathbf{a}+t\mathbf{b}\mid t\in\mathbb{R}\}

where a and b are given vectors in Rn with b non-zero. The vector b describes the direction of the line, and a is a point on the line. Different choices of a and b can yield the same line.

Projective geometry

In projective geometry, a line is similar to that in Euclidean geometry but has slightly different properties. In many models of projective geometry, the idea of the line rarely conforms to the notion of the "straight curve" as it is visualised in Euclidean geometry. The Poincaré half-plane model is a typical example of this.

Geodesics

The "straightness" of a line, interpreted as the property that it minimizes distances between its points, can be generalized and leads to the concept of geodesics on differentiable manifolds.

See also

Notes

  1. ^ Faber, Appendix A, p. 291.
  2. ^ Faber, Part III, p. 95.
  3. ^ Faber, Part III, p. 108.
  4. ^ Faber, Appendix B, p. 300.
  5. ^ Faber, Appendix B, p. 303.

References

  • Faber, Richard L. (1983). Foundations of Euclidean and Non-Euclidean Geometry. New York, United States: Marcel Dekker. ISBN 0-8247-1748-1. 

External links


Best of the Web: straight-line
Top

Some good "straight-line" pages on the web:


Math
mathworld.wolfram.com
 
Shopping: straight-line
Top
 
 

 

Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
Real Estate Dictionary. Dictionary of Real Estate Terms. Copyright © 2004 by Barron's Educational Series, Inc. All rights reserved.  Read more
WordNet. WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Line (geometry)" Read more