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A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes "straight curves"). In Euclidean geometry, exactly one line can be found that passes through any two points. The line provides the shortest connection between the points. In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...
A spatial point is an entity with a location in space but no extent (volume, area or length). ...
Three or more points that lie on the same line are called collinear. Two different lines can either be parallel and never meet, or may intersect at one and only one point. Two planes intersect in at most one line). Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
The term intersection can mean: a road junction, where two roads intersect each other, such as a roundabout intersection; in mathematics, the set in which two or more other sets intersect each other; see intersection (set theory); a movie; see Intersection (movie). ...
Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ...
Lines in a Cartesian plane can be described algebraically by linear equations and linear functions. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
bnrgljabvkfjabvgkjavgbkjavgkjA linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. ...
A linear function is a mathematical function term of the form: f(x) = m x + c where c is a constant. ...
This intuitive concept of a line can be formalized in various ways. If geometry is developed axiomatically (as in Euclid's Elements and later in David Hilbert's Foundations of Geometry), then lines are not defined at all, but characterized axiomatically by their properties. "Everything that satisfies the axioms for a line is a line." While Euclid did define a line as "length without breadth", he did not use this rather obscure definition in his later development. Table of Geometry, from the 1728 Cyclopaedia. ...
Euclid Euclid of Alexandria (Greek: ) (ca. ...
Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Egypt during the early 3rd century BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems) and proofs thereof. ...
David Hilbert David Hilbert (January 23, 1862, Wehlau, East Prussia–February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ...
In Euclidean space Rn (and analogously in all other vector spaces), we define a line L as a subset of the form In mathematics, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ...
Vector spaces (or linear spaces) are spaces whose elements, known as vectors, can be scaled and added; all linear combinations can be formed. ...
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. Vector spaces (or linear spaces) are spaces whose elements, known as vectors, can be scaled and added; all linear combinations can be formed. ...
In a two-dimensional space, such as the plane, two different lines must either be parallel lines or must intersect at one point. In higher-dimensional spaces however, two lines may do neither, and two such lines are called skew lines. Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
In geometry, two lines are said to be skew lines if they do not intersect but are not parallel. ...
In R2, every line L is described by a linear equation of the form
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. In mathematics, a coefficient is a multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. ...
bnrgljabvkfjabvgkjavgbkjavgkjA linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. ...
Look up Slope in Wiktionary, the free dictionary The slope or the gradient is commonly used to describe the measurement of the steepness, incline or grade of a straight line. ...
In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that f(x) = 0. ...
The y-intercept in 2-dimensional space is the point where the graph of a function or relationship intercepts the y-axis of the coordinate system. ...
(This page refers to eccentricity in mathematics. ...
The word infinity comes from the Latin infinitas or unboundedness. It refers to several distinct concepts which arise in theology, philosophy, mathematics and everyday life. ...
More abstractly, one usually thinks of the real line as the prototype of a line, and assumes that the points on a line stand in a one-to-one correspondence with the real numbers. However, one could also use the hyperreal numbers for this purpose, or even the long line of topology. In mathematics, the real line is simply the set of real numbers. ...
In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ...
In mathematics, particularly in non-standard analysis and mathematical logic, hyperreal numbers or nonstandard reals (usually denoted as *R) denote an ordered field which is a proper extension of the ordered field of real numbers R and which satisfies the transfer principle. ...
In topology, the long line is a topological space analogous to the real line, but much longer. ...
Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ...
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. In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. Definition of geodesic depends on the type of curved space. If the space carries a natural metric then geodesics are defined to be (locally) the shortest path between points on the space. ...
On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space. ...
Line segment
In mathematics, a line segment is a part of a line that is bounded by two end points. See also interval (mathematics). Euclid, detail from The School of Athens by Raphael. ...
The word point can refer to: a location in physical space a unit of angular measurement; see navigation point is a typographic unit of measure in typography equal inch or sometimes approximated as inch; on computer displays it should be equal to point in typography if the correct display resolution...
In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ...
When the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal. Look up Polygon in Wiktionary, the free dictionary. ...
Edge may have one of the following special meanings, in addition to its dictionary definition: // Computer Science In image processing, an edge is a position in a digital image where the luminous intensity changes sharply. ...
In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ...
The midpoint of a line segment is its 'middle' point: the unique point at an equal distance from the two end points.
A line segment starts at a fixed point and ends at a fixed point.
Ray In Euclidean geometry, a ray, or half-line, given two distinct points A (the origin) and B on the ray, is the set of points C on the line containing points A and B such that A is not strictly between C and B. Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...
Point can refer to: Look up Point in Wiktionary, the free dictionary // Mathematics In mathematics: Point (geometry), an entity that has a location in space but no extent Fixed point (mathematics), a point that is mapped to itself by a mathematical function Point at infinity Point group Point charge, an...
O----O-----*---> A B C In geometric optics a ray or a (light) beam is a line or curve that describes the direction in which light or other electromagnetic radiation is propagated. The ray is perpendicular to the wavefront in wave optics. See also list of optical topics. ...
In optics, a ray is an idealized narrow beam of light. ...
Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. ...
Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields. ...
Perpendicular is a geometric term that may be used as a noun or adjective. ...
In geometrical optics, a wave front (or crest of the wave) is defined as the locus of points having the same phase of vibration. ...
A wave is a disturbance that propagates through space, often transferring energy. ...
Table of Opticks, 1728 Cyclopaedia Optics (appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ...
In most media, light rays are straight lines. Light passing from one medium to another undergoes refraction or total internal reflection following Snell's law. The straw seems to be broken, due to refraction of light as it emerges into the air. ...
The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. ...
Snells law is the simple formula used to calculate the refraction of light when travelling between two media of differing refractive index. ...
See also The word linear comes from the Latin word linearis, which means created by lines. ...
bnrgljabvkfjabvgkjavgbkjavgkjA linear equation is an equation involving only the sum of constants or products of constants and the first power of a variable. ...
A linear function is a mathematical function term of the form: f(x) = m x + c where c is a constant. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesnt cover the terminology of differential topology. ...
In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ...
In geometry, the relations of incidence are those such as lies on between points and lines (as in point P lies on line L), and intersects (as in line L1 intersects line L2, in three-dimensional space). ...
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