Position (geometry)In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a pointP in space. Its length represents the distance in relation to an arbitrary reference originO, and its direction represents the angular orientation with respect to given reference axes.
Translation (geometry)In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry. A translation is an isometry that displaces the original figure according to a direction, a sense, and a length (vector).
Line (geometry)Straight figure with zero width and depth A red line near the origin on the two-dimensional Cartesian coordinate system In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve and an idealisation of such physical objects as a straightedge, a taut string, or a ray of light. Lines are spaces of dimension one, which may be embedded in spaces of dimension two, three, or higher.
Scalar multiplicationIn mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction.
Vector quantityIn the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. It is typically formulated as the product of a unit of measurement and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction. For example, a position vector in physical space may be expressed as threeCartesian coordinates with SI unit of meters.
Line segmentIn geometry, a line segment is a part of a straight line that is bounded by two distinct endpoints (its extreme points), and contains every point on the line that is between its endpoints. It is a special case of an arc, with zero curvature. The length of a line segment is given by the Euclidean distance between its endpoints.
Scaling (geometry)In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar.
GeometryBranch of mathematics GeometryProjecting a sphere to a plane Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry ConceptsFeaturesDimension Straightedge and compass constructions Angle Polytope Centroid Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line Line segment Ray Curve Geodesic Length Two-dimensional Surface Plane Area Polygon Simple Convex Concave Star Regular Reuleaux Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Reuleaux Hyperbolic Ideal Spherical Quadrilateral Parallelogram Rectangle Square Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Star Toroidal Ideal Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov vte Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
Euclidean vectorIn mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a directed line segment.
Equipollence (geometry)In Euclidean geometry, equipollence is a homogeneous relation between directed line segments. Two segments are said to be equipollent when they have the same length and direction. Two equipollent segments are parallel but not necessarily colinear nor overlapping. For example, a segment AB, from point A to point B, has the opposite direction to segment BA; thus AB and BA are not equipollent.*As an Amazon Associate I earn from qualifying purchases.