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# Cartesian coordinate system

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 from the point to two fixed perpendicular directed lines, measured in the same unit of length. [1]

110 relations: Abscissa, Affine transformation, Algebra, Analytic geometry, Array data type, Astronomy, Bijection, Binary relation, Calculus, Cartesian product, Clockwise, Complex number, Computational geometry, Computer graphics, Computer programming, Computer-aided design, Coordinate rotations and reflections, Coordinate system, Curve, Cylindrical coordinate system, Dauphin of France, Determinant, Differential geometry, Dimension, 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, Half-space (geometry), Henry Margenau, Heraldry, Herman Feshbach, Horizontal and vertical, Horizontal plane, Hyperplane, Identity matrix, If and only if, Image processing, Imaginary unit, Index finger, Isaac Newton, ... Expand index (60 more) »

## Abscissa

In mathematics, an abscissa (plural abscissae or abscissæ or abscissas) is the perpendicular distance of a point from the vertical axis.

## Affine transformation

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

## Algebra

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

## Analytic geometry

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

## Array data type

In computer science, an array type is a data type that is meant to describe a collection of elements (values or variables), each selected by one or more indices (identifying keys) that can be computed at run time by the program.

## Astronomy

Astronomy is a natural science which is the study of celestial objects (such as stars, galaxies, planets, moons, asteroids, comets and nebulae), the physics, chemistry, and evolution of such objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explosions, gamma ray bursts, and cosmic microwave background radiation.

## Bijection

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

## Binary relation

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

## Calculus

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

## Cartesian product

In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set or simply product) from multiple sets.

## Clockwise

Circular motion can occur in two possible directions.

## Complex number

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

## Computational geometry

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

## Computer graphics

Computer graphics are pictures and movies created using computers - usually referring to image data created by a computer specifically with help from specialized graphical hardware and software.

## Computer programming

Computer programming (often shortened to programming) is a process that leads from an original formulation of a computing problem to executable computer programs.

## Computer-aided design

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

## 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.

## Coordinate system

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

## Curve

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

## 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.

## Dauphin of France

The Dauphin of France (Dauphin de France)—strictly The Dauphin of Viennois (Dauphin de Viennois)—was the title given to the heir apparent to the throne of France from 1350 to 1791 and 1824 to 1830.

## Determinant

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

## 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.

## 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.

## Engineering

Engineering is the application of mathematics, empirical evidence and scientific, economic, social, and practical knowledge in order to invent, design, build, maintain, research, and improve, structures, machines, tools, systems, components, materials, and processes.

## Equation

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

## Euclidean distance

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

## Euclidean geometry

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

## 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.

## Euclidean space

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

## 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 and can be added to other vectors according to vector algebra.

## Framebuffer

A framebuffer (frame buffer, or sometimes framestore) is a portion of RAM containing a bitmap that is driven to a video display from a memory buffer containing a complete frame of data.

## Frans van Schooten

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

## Glide reflection

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

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm von Leibniz (also Godefroi Guillaume Leibnitz,; or; July 1, 1646 – November 14, 1716) was a German polymath and philosopher, and to this day he occupies a prominent place in the history of mathematics and the history of philosophy.

## Graph of a function

In mathematics, the graph of a function f is the collection of all ordered pairs.

## Group theory

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

## Half-space (geometry)

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.

## Henry Margenau

Henry Margenau (1901 - February 8, 1997) was a German-U.S. physicist, and philosopher of science.

## Heraldry

Heraldry is the profession, study, or art of creating, granting, and blazoning arms and ruling on questions of rank or protocol, as exercised by an officer of arms.

## Herman Feshbach

Herman Feshbach (February 2, 1917, in New York City &mdash; 22 December, 2000, in Cambridge, Massachusetts) was an American physicist.

## Horizontal and vertical

The usage of the inter-related terms horizontal and vertical varies with context, There are important symmetries and asymmetries between the two terms which change as one goes from two to three dimensions, from a flat earth scenario to the spherical earth one.

## 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&mdash; in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.

## Hyperplane

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

## Identity matrix

In linear algebra, the identity matrix or unit matrix of size n is the n &times; n square matrix with ones on the main diagonal and zeros elsewhere.

## 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.

## Image processing

In imaging science, image processing is processing of images using mathematical operations by using any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or a set of characteristics or parameters related to the image.

## Imaginary unit

The term imaginary unit or unit imaginary number refers to a solution to the equation.

## Index finger

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

## Isaac Newton

Sir Isaac Newton (25 December 164220 March 1726/7) was an English physicist and mathematician (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution.

## 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.

## La Géométrie

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

## Latin

Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.

## Latinisation of names

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

## 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.

## Linear algebra

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces.

## Mathematician

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

## Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is interpreted and manipulated in certain prescribed ways.

## 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.

## Number

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

## Ordered pair

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

## Ordinate

In mathematics, ordinate most often refers to that element of an ordered pair which is plotted on the vertical axis of a two-dimensional Cartesian coordinate system, as opposed to the abscissa.

## 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.

## 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.

## Orthogonal coordinates

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

## Orthogonality

In mathematics, orthogonality is the relation of two lines at right angles to one another (perpendicularity), and the generalization of this relation into n dimensions; and to a variety of mathematical relations thought of as describing non-overlapping, uncorrelated, or independent objects of some kind.

## Perpendicular

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

## Perspective (graphical)

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

## Philip M. Morse

Philip McCord Morse (August 6, 19035 September 1985), was an American physicist, administrator and pioneer of operations research (OR) in World War II.

## Philosopher

A philosopher, in a broad sense, is someone who studies philosophy.

## Physics

Physics (from knowledge of nature, from φύσις phúsis "nature") is the natural science that involves the study of 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 through space and time, along with related concepts such as 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." More broadly, it is the general analysis of nature, conducted in order 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, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the scientific revolution in the 17th century, the natural sciences emerged as unique research programs 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 of other sciences while opening new avenues of research in areas such as mathematics and philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or 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.

## Pierre de Fermat

Pierre de Fermat (17 August 1601 – 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.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface.

## Point (geometry)

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

## 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.

## 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.

## Prime meridian

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

## Projection (linear algebra)

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

## Pythagorean theorem

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

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

## Quaternion

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

## Real coordinate space

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

## Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

## Record (computer science)

In computer science, a record (also called struct or compound data) is a basic data structure (a tuple may or may not be considered a record, and vice versa, depending on conventions and the programming language at hand).

## 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.

## René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 159611 February 1650) was a French philosopher, mathematician, and scientist who spent about 20 years of his life in the Dutch Republic.

## Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in three dimensions.

## Rigid transformation

In mathematics, a rigid transformation (isometry) of a vector space preserves distances between every pair of points.

## Roman numerals

Roman numerals, the numeric system used in ancient Rome, employs combinations of letters from the Latin alphabet to signify values.

## Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

## Rotation matrix

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

## 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.

## Sign (mathematics)

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

## Space (mathematics)

In mathematics, a space is a set (sometimes called a universe) with some added structure.

## 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.

## Standard basis

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

## Subscript and superscript

A subscript or superscript is a number, figure, symbol, or indicator that is smaller than the normal line of type and is set slightly below or above it.

## Thumb

The thumb is the first digit of the hand.

## Time

Time is a measure in which events can be ordered from the past through the present into the future, and also the measure of durations of events and the intervals between them.

## Translation (geometry)

In Euclidean geometry, a translation is a function that moves every point a constant distance in a specified direction.

## Transpose

In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr, tA or At) created by any one of the following equivalent actions.

## Tuple

A tuple is a finite ordered list of elements.

## 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.

## Unit circle

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

## Unit hyperbola

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

## Unit vector

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

## Units of measurement

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

## Versor

Versors are an algebraic parametrisation of rotations.

## Vertical direction

In astronomy, geography, geometry and related sciences and contexts, a direction passing by a given point is said to be vertical if it is locally aligned with the gradient of the gravity field, i.e., with the direction of the gravitational force (per unit mass, i.e. gravitational acceleration vector) at that point.

## 3D projection

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

## References

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