HOME TheInfoList.com
Providing Lists of Related Topics to Help You Find Great Stuff
[::MainTopicLength::#1500] [::ListTopicLength::#1000] [::ListLength::#15] [::ListAdRepeat::#3]

picture info

Half Line
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 17th century, lines were defined in this manner: "The 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
[...More...]

"Half Line" on:
Wikipedia
Google
Yahoo

picture info

Symmetry
SYMMETRY (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection , rotation or scaling . Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together. Mathematical symmetry may be observed with respect to the passage of time ; as a spatial relationship ; through geometric transformations ; through other kinds of functional transformations; and as an aspect of abstract objects , theoretic models , language , music and even knowledge itself
[...More...]

"Symmetry" on:
Wikipedia
Google
Yahoo

picture info

Similarity (geometry)
Two geometrical objects are called SIMILAR if they both have the same shape , or one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation , rotation and reflection . This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other. A modern and novel perspective of similarity is to consider geometrical objects similar if one appears congruent to the other when zoomed in or out at some level. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other
[...More...]

"Similarity (geometry)" on:
Wikipedia
Google
Yahoo

picture info

One-dimensional Space
In physics and mathematics , a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a ONE-DIMENSIONAL SPACE . An example of a one-dimensional space is the number line , where the position of each point on it can be described by a single number. In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself. Similarly, the projective line over k is a one-dimensional space. In particular, if k = ℂ, the complex numbers , then the complex projective line P1(ℂ) is one-dimensional with respect to ℂ, even though it is also known as the Riemann sphere . More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring
[...More...]

"One-dimensional Space" on:
Wikipedia
Google
Yahoo

picture info

Point (geometry)
In modern mathematics , a POINT refers usually to an element of some set called a space . More specifically, in Euclidean geometry
Euclidean geometry
, a point is a primitive notion upon which the geometry is built, meaning that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms , that it must satisfy. In particular, the geometric points do not have any length , area , volume or any other dimensional attribute. A common interpretation is that the concept of a point is meant to capture the notion of a unique location in Euclidean space
Euclidean space

[...More...]

"Point (geometry)" on:
Wikipedia
Google
Yahoo

picture info

Ray (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 17th century, lines were defined in this manner: "The 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
[...More...]

"Ray (geometry)" on:
Wikipedia
Google
Yahoo

picture info

Congruence (geometry)
In geometry , two figures or objects are CONGRUENT if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called CONGRUENT if, and only if, one can be transformed into the other by an isometry , i.e., a combination of RIGID MOTIONS, namely a translation , a rotation , and a reflection . This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted. In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects
[...More...]

"Congruence (geometry)" on:
Wikipedia
Google
Yahoo

Vertex (geometry)
In geometry , a VERTEX (plural: VERTICES or VERTEXES) is a point where two or more curves , lines , or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. CONTENTS* 1 Definition * 1.1 Of an angle * 1.2 Of a polytope * 1.3 Of a plane tiling * 2 Principal vertex * 2.1 Ears * 2.2 Mouths * 3 Number of vertices of a polyhedron * 4 Vertices in computer graphics * 5 References * 6 External links DEFINITIONOF AN ANGLE A vertex of an angle is the endpoint where two line segments or rays come together. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place
[...More...]

"Vertex (geometry)" on:
Wikipedia
Google
Yahoo

picture info

Diagonal
In geometry , a DIAGONAL is a line segment joining two vertices of a polygon or polyhedron , when those vertices are not on the same edge . Informally, any sloping line is called diagonal. The word "diagonal" derives from the ancient Greek διαγώνιος diagonios, "from angle to angle" (from διά- dia-, "through", "across" and γωνία gonia, "angle", related to gony "knee"); it was used by both Strabo
Strabo
and Euclid
Euclid
to refer to a line connecting two vertices of a rhombus or cuboid , and later adopted into Latin as diagonus ("slanting line"). In matrix algebra , a diagonal of a square matrix is a set of entries extending from one corner to the farthest corner. There are also other, non-mathematical uses
[...More...]

"Diagonal" on:
Wikipedia
Google
Yahoo

picture info

Orthogonal
In mathematics , ORTHOGONALITY is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms . Two elements u and v of a vector space with bilinear form B are ORTHOGONAL when B(u,v) = 0. When the bilinear form corresponds to a pseudo- Euclidean space
Euclidean space
, there are non-perpendicular vectors that are hyperbolic-orthogonal . In the case of function spaces , families of orthogonal functions are used to form a basis
[...More...]

"Orthogonal" on:
Wikipedia
Google
Yahoo

picture info

Perpendicular
In elementary geometry , the property of being PERPENDICULAR (PERPENDICULARITY) is the relationship between two lines which meet at a right angle (90 degrees ). The property extends to other related geometric objects . A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles . Perpendicularity can be shown to be symmetric , meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order. Perpendicularity easily extends to segments and rays
[...More...]

"Perpendicular" on:
Wikipedia
Google
Yahoo

picture info

Parallel (geometry)
In geometry , PARALLEL lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space
Euclidean space
that do not share a point are said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines . Parallel planes are planes in the same three-dimensional space that never meet. Parallel lines are the subject of Euclid
Euclid
's parallel postulate . Parallelism is primarily a property of affine geometries and Euclidean space is a special instance of this type of geometry. Some other spaces, such as hyperbolic space , have analogous properties that are sometimes referred to as parallelism
[...More...]

"Parallel (geometry)" on:
Wikipedia
Google
Yahoo

picture info

Length
In geometric measurements, LENGTH is the most extended dimension of an object. In the International System of Quantities , length is any quantity with dimension distance. In other contexts "length" is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness. Length
Length
may be distinguished from height , which is vertical extent, and width or breadth, which are the distance from side to side, measuring across the object at right angles to the length. Length
Length
is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed). In most systems of measurement , the unit of length is a base unit , from which other units are derived. The metric length of one kilometre is equivalent to the imperial measurement of 0.62137 miles
[...More...]

"Length" on:
Wikipedia
Google
Yahoo

picture info

Two-dimensional Space
In physics and mathematics , TWO-DIMENSIONAL SPACE or BI-DIMENSIONAL SPACE is a geometric model of the planar projection of the physical universe . The two dimensions are commonly called length and width. Both directions lie in the same plane . A sequence of n real numbers can be understood as a location in n-dimensional space. When n = 2, the set of all such locations is called two-dimensional space or bi-dimensional space, and usually is thought of as a Euclidean space
Euclidean space

[...More...]

"Two-dimensional Space" on:
Wikipedia
Google
Yahoo

picture info

Square
In geometry , a SQUARE is a regular quadrilateral , which means that it has four equal sides and four equal angles (90-degree angles, or right angles ). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted {displaystyle square } ABCD
[...More...]

"Square" on:
Wikipedia
Google
Yahoo

picture info

Parallelogram
In Euclidean geometry , a PARALLELOGRAM is a simple (non-self-intersecting ) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped . The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel lines") reflects the definition
[...More...]

"Parallelogram" on:
Wikipedia
Google
Yahoo
.