• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Logic and Proof In logic (and mathematics) one often has to prove
Logic and Proof In logic (and mathematics) one often has to prove

Lesson 1 - Lincoln Middle School
Lesson 1 - Lincoln Middle School

Geometry
Geometry

Properties, Postulates, and Theorems for Proofs
Properties, Postulates, and Theorems for Proofs

Taxicab Triangle Incircles and Circumcircles
Taxicab Triangle Incircles and Circumcircles

Matt Wolf - CB East Wolf
Matt Wolf - CB East Wolf

Geometric Constructions for Love and Money
Geometric Constructions for Love and Money

Geometry
Geometry

Time - UWM
Time - UWM

... With the adoption of a new textbook series for the Milwaukee Public Schools in the Spring of 2008, it became necessary to design pacing guides for these textbooks. The following is Draft One of the Pacing Guide for Discovering Geometry. Just like the headers to this document state, this is a draft. ...
5 Properties of shapes and solids
5 Properties of shapes and solids

File
File

Nonoverlap of the Star Unfolding
Nonoverlap of the Star Unfolding

Document
Document

1. Motivation - Singapore Mathematical Society
1. Motivation - Singapore Mathematical Society

Postulate 3
Postulate 3

... in a parallelogram the opposite sides are of equal length in a parallelogram the opposite sides are congruent if the diagonal bisect teach other then the quadrilateral is a parallelogram if a quadrilateral is a parallelogram then its consecutive sides are complementary a quadrilateral is a parallel ...
Lesson 23: Base Angles of Isosceles Triangles
Lesson 23: Base Angles of Isosceles Triangles

Geometry Module 1, Topic D, Lesson 23: Teacher
Geometry Module 1, Topic D, Lesson 23: Teacher

Writing Decimals as Fractions
Writing Decimals as Fractions

...  Chapter 5 TEST Tuesday ...
Chapter 12 - BISD Moodle
Chapter 12 - BISD Moodle

Lesson 23-2
Lesson 23-2

Teacher Instructions for: Straw Triangles
Teacher Instructions for: Straw Triangles

GCSE Specification and Revision Notes
GCSE Specification and Revision Notes

Geometry Midterm
Geometry Midterm

Symplectic structures -- a new approach to geometry.
Symplectic structures -- a new approach to geometry.

February 24, 2010
February 24, 2010

< 1 ... 31 32 33 34 35 36 37 38 39 ... 604 >

Line (geometry)



The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth. Lines are an idealization of such objects. Until the seventeenth century, lines were defined in this manner: ""The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width. […] The straight line is that which is equally extended between its points""Euclid described a line as ""breadthless length"" which ""lies equally with respect to the points on itself""; he introduced several postulates as basic unprovable properties from which he constructed the geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of nineteenth century (such as non-Euclidean, projective and affine geometry).In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it.When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object). The properties of lines are then determined by the axioms which refer to them. One advantage to this approach is the flexibility it gives to users of the geometry. Thus in differential geometry a line may be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and, for example, permits physicists to think of the path of a light ray as being a line.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, but unlike lines they may be none of these, if they are coplanar and either do not intersect or are collinear.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report