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Cartesian coordinate system

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A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. [1]

112 relations: Abscissa and ordinate, Absolute value (algebra), Affine plane, Affine transformation, Algebra, Analytic geometry, Array data type, Astronomy, Bijection, Binary relation, Bracket, Calculus, Cartesian product, Clockwise, Complex analysis, Complex number, Computational geometry, Computer graphics, Computer programming, Computer-aided design, Coordinate rotations and reflections, Coordinate system, Curve, Cylindrical coordinate system, Determinant, Differential geometry, Digital image processing, Dimension, Distance from a point to a line, Engineering, Equation, Euclidean distance, Euclidean geometry, Euclidean plane isometry, Euclidean space, Euclidean vector, Framebuffer, Frans van Schooten, Glide reflection, Gottfried Wilhelm Leibniz, Graph of a function, Group theory, Heraldry, Horizontal and vertical, Horizontal plane, Hosohedron, Hyperplane, Identity matrix, If and only if, Imaginary unit, ..., Index finger, Isaac Newton, Jones diagram, La Géométrie, Latinisation of names, Line (geometry), Linear algebra, Mathematician, Matrix (mathematics), Middle finger, Number, Ordered pair, Origin (mathematics), Orthant, Orthogonal coordinates, Orthogonality, Perpendicular, Perspective (graphical), Philosopher, Physics, Pierre de Fermat, Plane (geometry), Point (geometry), Polar coordinate system, Pressure, Prime meridian, Projection (linear algebra), Pythagorean theorem, Quadrant (plane geometry), Quaternion, Real coordinate space, Real number, Record (computer science), Reflection (mathematics), René Descartes, Right angle, Right-hand rule, Rigid transformation, Roman numerals, Rotation (mathematics), Rotation matrix, Shear mapping, Sign (mathematics), Spherical coordinate system, Standard basis, Subscript and superscript, Three-dimensional space, Thumb, Time, Translation (geometry), Transpose, Tuple, Two-dimensional space, Unit circle, Unit hyperbola, Unit of length, Unit of measurement, Unit square, Unit vector, Vector space, Versor, 3D projection. Expand index (62 more) »

Abscissa and ordinate

In mathematics, the abscissa (plural abscissae or abscissæ or abscissas) and the ordinate are respectively the first and second coordinate of a point in a coordinate system.

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Absolute value (algebra)

In mathematics, an absolute value is a function which measures the "size" of elements in a field or integral domain.

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Affine plane

In geometry, an affine plane is a two-dimensional affine space.

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Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

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Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Array data type

Language support for array types may include certain built-in array data types, some syntactic constructions (array type constructors) that the programmer may use to define such types and declare array variables, and special notation for indexing array elements.

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Astronomy

Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

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Bijection

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Bracket

A bracket is a tall punctuation mark typically used in matched pairs within text, to set apart or interject other text.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Cartesian product

In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.

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Clockwise

Two-dimensional rotation can occur in two possible directions.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

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Computer graphics

Computer graphics are pictures and films created using computers.

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Computer programming

Computer programming is the process of building and designing an executable computer program for accomplishing a specific computing task.

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Computer-aided design

Computer-aided design (CAD) is the use of computer systems to aid in the creation, modification, analysis, or optimization of a design.

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Coordinate rotations and reflections

In geometry, two-dimensional coordinate rotations and reflections are two kinds of Euclidean plane isometries which are related to one another.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

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Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Digital image processing

In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.

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Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Distance from a point to a line

The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry.

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Engineering

Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

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Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

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Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Euclidean plane isometry

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical properties such as length.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Framebuffer

A framebuffer (frame buffer, or sometimes framestore) is a portion of RAM containing a bitmap that drives a video display.

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Frans van Schooten

Franciscus van Schooten (1615, Leiden – 29 May 1660, Leiden) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes.

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Glide reflection

In 2-dimensional geometry, a glide reflection (or transflection) is a type of opposite isometry of the Euclidean plane: the composition of a reflection in a line and a translation along that line.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Heraldry

Heraldry is a broad term, encompassing the design, display, and study of armorial bearings (known as armory), as well as related disciplines, such as vexillology, together with the study of ceremony, rank, and pedigree.

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Horizontal and vertical

The usage of the inter-related terms horizontal and vertical as well as their symmetries and asymmetries vary with context (e.g. two vs. three dimensions or calculations using a flat earth approximation vs. spherical earth).

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Horizontal plane

In geometry, physics, astronomy, geography, and related sciences, a plane is said to be horizontal at a given point if it is perpendicular to the gradient of the gravity field at that point – in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.

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Hosohedron

In geometry, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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Index finger

The index finger (also referred to as forefinger, first finger, pointer finger, trigger finger, digitus secundus, digitus II, and many other terms), is the first finger and the second digit of a human hand.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Jones diagram

A Jones diagram is a type of Cartesian graph developed by Loyd A. Jones in the 1940s, where each axis represents a different variable.

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La Géométrie

La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes.

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Latinisation of names

Latinisation or Latinization is the practice of rendering a non-Latin name (or word) in a Latin style.

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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.

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Middle finger

The middle finger, long finger, or tall finger is the third digit of the human hand, located between the index finger and the ring finger.

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Number

A number is a mathematical object used to count, measure and also label.

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Ordered pair

In mathematics, an ordered pair (a, b) is a pair of objects.

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Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space.

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Orthant

In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.

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Orthogonal coordinates

In mathematics, orthogonal coordinates are defined as a set of d coordinates q.

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Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

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Philosopher

A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside either theology or science.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space.

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Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

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Pressure

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

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Prime meridian

A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Quadrant (plane geometry)

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes.

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Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

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Real coordinate space

In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Record (computer science)

In computer science, a record (also called a structure, struct, or compound data) is a basic data structure.

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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

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Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation conventions for the vector cross product in three dimensions.

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Rigid transformation

In mathematics, a rigid transformation or Euclidean isometry of a Euclidean space preserves distances between every pair of points.

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Roman numerals

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.

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Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

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Rotation matrix

In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

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Shear mapping

In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction.

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Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.

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Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

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Standard basis

In mathematics, the standard basis (also called natural basis) for a Euclidean space is the set of unit vectors pointing in the direction of the axes of a Cartesian coordinate system.

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Subscript and superscript

A subscript or superscript is a character (number, letter or symbol) that is (respectively) set slightly below or above the normal line of type.

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Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

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Thumb

The thumb is the first digit of the hand.

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Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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Translation (geometry)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

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Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).

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Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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Unit hyperbola

In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.

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Unit of length

A unit of length refers to any discrete, pre-established length or distance having a constant magnitude which is used as a reference or convention to express linear dimension.

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Unit of measurement

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

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Unit square

In mathematics, a unit square is a square whose sides have length.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Versor

In mathematics, a versor is a quaternion of norm one (a unit quaternion).

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3D projection

3D projection is any method of mapping three-dimensional points to a two-dimensional plane.

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References

[1] https://en.wikipedia.org/wiki/Cartesian_coordinate_system

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