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57-688: American Tourister is a brand of luggage owned by Samsonite . Brothers Sol and Irving Koffler founded American Luggage Works in Providence, Rhode Island , United States in 1933. In 1993, American Tourister was acquired by Astrum International, which also owns Samsonite. Astrum was renamed as the Samsonite Corporation two years later. American Tourister's products include backpacks, suitcases and wallets. Today, American Tourister products are priced lower than Samsonite products. This United States manufacturing company–related article

114-486: A baggage claim or reclaim area is an area where arriving passengers claim checked-in baggage after disembarking from an airline flight. At most airports and many train stations, baggage is delivered to the passenger on a baggage carousel . Left luggage, also luggage storage or bag storage, is a place where one can temporarily store one's luggage so as to not have to carry it. Left luggage is not synonymous with lost luggage . Often at an airport or train station there may be

171-464: A coordinate frame called the Cartesian frame . Similarly, the position of any point in three-dimensional space can be specified by three Cartesian coordinates , which are the signed distances from the point to three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n -dimensional Euclidean space for any dimension n . These coordinates are

228-497: A plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates , which are the signed distances to the point from two fixed perpendicular oriented lines , called coordinate lines , coordinate axes or just axes (plural of axis ) of the system. The point where the axes meet is called the origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis . The combination of origin and basis forms

285-567: A "macho thing" where "men would not accept suitcases with wheels". Others attribute the late invention to "the abundance of luggage porters with carts in the 1960s, the ease of curbside drop-offs at much smaller airports and the heavy iron casters then available." Passengers are allowed to carry a limited number of smaller bags with them in the vehicle, these are known as hand luggage (more commonly referred to as carry-on in North America ), and contain valuables and items needed during

342-521: A , b ) to the Cartesian coordinates of every point in the set. That is, if the original coordinates of a point are ( x , y ) , after the translation they will be ( x ′ , y ′ ) = ( x + a , y + b ) . {\displaystyle (x',y')=(x+a,y+b).} To rotate a figure counterclockwise around the origin by some angle θ {\displaystyle \theta }

399-449: A diagram ( 3D projection or 2D perspective drawing ) shows the x - and y -axis horizontally and vertically, respectively, then the z -axis should be shown pointing "out of the page" towards the viewer or camera. In such a 2D diagram of a 3D coordinate system, the z -axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective . In any diagram or display,

456-407: A division of space into eight regions or octants , according to the signs of the coordinates of the points. The convention used for naming a specific octant is to list its signs; for example, (+ + +) or (− + −) . The generalization of the quadrant and octant to an arbitrary number of dimensions is the orthant , and a similar naming system applies. The Euclidean distance between two points of

513-433: A number line. For any point P , a line is drawn through P perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The two numbers, in that chosen order, are the Cartesian coordinates of P . The reverse construction allows one to determine the point P given its coordinates. The first and second coordinates are called the abscissa and the ordinate of P , respectively; and

570-1238: A point P can be taken as the distance from P to the plane defined by the other two axes, with the sign determined by the orientation of the corresponding axis. Each pair of axes defines a coordinate plane . These planes divide space into eight octants . The octants are: ( + x , + y , + z ) ( − x , + y , + z ) ( + x , − y , + z ) ( + x , + y , − z ) ( + x , − y , − z ) ( − x , + y , − z ) ( − x , − y , + z ) ( − x , − y , − z ) {\displaystyle {\begin{aligned}(+x,+y,+z)&&(-x,+y,+z)&&(+x,-y,+z)&&(+x,+y,-z)\\(+x,-y,-z)&&(-x,+y,-z)&&(-x,-y,+z)&&(-x,-y,-z)\end{aligned}}} The coordinates are usually written as three numbers (or algebraic formulas) surrounded by parentheses and separated by commas, as in (3, −2.5, 1) or ( t , u + v , π /2) . Thus,

627-456: A point are ( x , y ) , then its distances from the X -axis and from the Y -axis are | y | and | x |, respectively; where | · | denotes the absolute value of a number. A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the axes ) that go through a common point (the origin ), and are pair-wise perpendicular; an orientation for each axis; and

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684-401: A point are usually written in parentheses and separated by commas, as in (10, 5) or (3, 5, 7) . The origin is often labelled with the capital letter O . In analytic geometry, unknown or generic coordinates are often denoted by the letters ( x , y ) in the plane, and ( x , y , z ) in three-dimensional space. This custom comes from a convention of algebra, which uses letters near the end of

741-472: A single unit of length for all three axes. As in the two-dimensional case, each axis becomes a number line. For any point P of space, one considers a plane through P perpendicular to each coordinate axis, and interprets the point where that plane cuts the axis as a number. The Cartesian coordinates of P are those three numbers, in the chosen order. The reverse construction determines the point P given its three coordinates. Alternatively, each coordinate of

798-546: A staffed 'left luggage counter' or simply a coin-operated or automated locker system. While threats of terrorism all around the globe have caused this type of public storage to decrease over the past few decades, the sharing economy is causing a revival of the industry. Driven in part by the rapid growth of Airbnb and homestay traveling in general, a number of services offering short-term luggage storage by utilizing unused space at local businesses such as hotels, restaurants and retail shops have emerged. Baggage can also refer to

855-498: A wheeled trunk in 1887, and a wheeled suitcase in 1945 – but these were not successfully commercialized. The first rolling suitcase was invented by a French engineer, Maurice Partiot, who was living in the USA at that time. The patent was registered n° 2 463 713, March 8, 1949. But the application was not pursued by its inventor and the patent lapsed in 1967. Bernard D. Sadow developed the first commercial rolling suitcase by applying for

912-460: Is a stub . You can help Misplaced Pages by expanding it . Luggage Baggage (not luggage), or baggage train , can also refer to the train of people and goods, both military and of a personal nature, which commonly followed pre-modern armies on campaign. Luggage has changed over time. Historically the most common types of luggage were chests or trunks made of wood or other heavy materials. These would be shipped by professional movers. Since

969-545: Is baggage that has a built-in or a removable battery within. It often includes features designed to help with travel, including GPS tracking and USB ports to charge electronics. Some bags include a WiFi hotspot and electric wheels for personal transportation. Several smart luggage companies have shut down as a result of a ban which came into effect in January 2018 on smart luggage with non-removable batteries being carried as check-in luggage on flights. In airport terminals,

1026-514: Is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see affine plane ). The Cartesian coordinates of

1083-879: Is the Cartesian version of Pythagoras's theorem . In three-dimensional space, the distance between points ( x 1 , y 1 , z 1 ) {\displaystyle (x_{1},y_{1},z_{1})} and ( x 2 , y 2 , z 2 ) {\displaystyle (x_{2},y_{2},z_{2})} is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 , {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}},} which can be obtained by two consecutive applications of Pythagoras' theorem. The Euclidean transformations or Euclidean motions are

1140-454: Is the set of all real numbers. In the same way, the points in any Euclidean space of dimension n be identified with the tuples (lists) of n real numbers; that is, with the Cartesian product R n {\displaystyle \mathbb {R} ^{n}} . The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate

1197-501: Is usually named after the coordinate which is measured along it; so one says the x-axis , the y-axis , the t-axis , etc. Another common convention for coordinate naming is to use subscripts, as ( x 1 , x 2 , ..., x n ) for the n coordinates in an n -dimensional space, especially when n is greater than 3 or unspecified. Some authors prefer the numbering ( x 0 , x 1 , ..., x n −1 ). These notations are especially advantageous in computer programming : by storing

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1254-690: The Second World War smaller and more lightweight suitcases and bags that can be carried by an individual have become the main form of luggage. According to the Oxford English Dictionary , the word baggage comes from the Old French bagage (from baguer 'tie up') or from bagues 'bundles'. It may also be related to the word bag . Also according to the Oxford English Dictionary,

1311-405: The xy -plane, yz -plane, and xz -plane. In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In that case the third coordinate may be called height or altitude . The orientation is usually chosen so that the 90-degree angle from the first axis to the second axis looks counter-clockwise when seen from

1368-416: The z -coordinate is sometimes called the applicate . The words abscissa , ordinate and applicate are sometimes used to refer to coordinate axes rather than the coordinate values. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants , each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals : I (where

1425-457: The ( bijective ) mappings of points of the Euclidean plane to themselves which preserve distances between points. There are four types of these mappings (also called isometries): translations , rotations , reflections and glide reflections . Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers (

1482-432: The 2004 version of their signature Silhouette line. These are otherwise similar in design to two-wheel roll-aboards, with a vertical orientation and a retracting handle, but are designed to be pushed beside or in front of the traveler, rather than pulled behind them. These are often referred to as "spinner" luggage, since they can spin about their vertical axis . Sadow attributes the late invention of luggage on wheels to

1539-406: The Cartesian system, commonly learn the order to read the values before cementing the x -, y -, and z -axis concepts, by starting with 2D mnemonics (for example, 'Walk along the hall then up the stairs' akin to straight across the x -axis then up vertically along the y -axis). Computer graphics and image processing , however, often use a coordinate system with the y -axis oriented downwards on

1596-506: The Travelpro company, which marketing the suitcases under the trademark "Rollaboard". The terms rollaboard and roll-aboard are used generically, however. While initially designed for carry-on use (to navigate through a large terminal), as implied by the analogous name, similar designs are also used for checked baggage . More recently, four-wheeled luggage with casters has become popular, notably since their use by Samsonite in

1653-406: The alphabet for unknown values (such as the coordinates of points in many geometric problems), and letters near the beginning for given quantities. These conventional names are often used in other domains, such as physics and engineering, although other letters may be used. For example, in a graph showing how a pressure varies with time , the graph coordinates may be denoted p and t . Each axis

1710-407: The computer display. This convention developed in the 1960s (or earlier) from the way that images were originally stored in display buffers . For three-dimensional systems, a convention is to portray the xy -plane horizontally, with the z -axis added to represent height (positive up). Furthermore, there is a convention to orient the x -axis toward the viewer, biased either to the right or left. If

1767-413: The coordinates both have positive signs), II (where the abscissa is negative − and the ordinate is positive +), III (where both the abscissa and the ordinate are −), and IV (abscissa +, ordinate −). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("north-east") quadrant. Similarly, a three-dimensional Cartesian system defines

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1824-455: The coordinates of a point as an array , instead of a record , the subscript can serve to index the coordinates. In mathematical illustrations of two-dimensional Cartesian systems, the first coordinate (traditionally called the abscissa ) is measured along a horizontal axis, oriented from left to right. The second coordinate (the ordinate ) is then measured along a vertical axis, usually oriented from bottom to top. Young children learning

1881-441: The coordinates of points of the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x + y = 4 ; the area , the perimeter and the tangent line at any point can be computed from this equation by using integrals and derivatives , in a way that can be applied to any curve. Cartesian coordinates are

1938-518: The discovery. The French cleric Nicole Oresme used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat. Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' La Géométrie was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify

1995-449: The first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards. (However, in some computer graphics contexts, the ordinate axis may be oriented downwards.) The origin is often labeled O , and the two coordinates are often denoted by the letters X and Y , or x and y . The axes may then be referred to as the X -axis and Y -axis. The choices of letters come from

2052-428: The following decades, as reflected in patents such as a 1948 US patent by Herbert Ernest Mingo, for a "device for the handling of trunks, suitcases, and the like". A US patent for a "luggage carriage" filed in 1949 (and published 1953), and another for a "luggage carriage harness", were both made by Kent R. Costikyan. However, the wheels were external to the suitcases. Patents had been published for wheeled luggage –

2109-487: The foundation of analytic geometry , and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra , complex analysis , differential geometry , multivariate calculus , group theory and more. A familiar example is the concept of the graph of a function . Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy , physics , engineering and many more. They are

2166-479: The ideas contained in Descartes's work. The development of the Cartesian coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz . The two-coordinate description of the plane was later generalized into the concept of vector spaces . Many other coordinate systems have been developed since Descartes, such as the polar coordinates for

2223-420: The invention. Sadow's four-wheeled suitcases, pulled using a loose strap, were later surpassed in popularity by suitcases that feature two wheels and are pulled in an upright position using a long handle. These were invented in 1987 by US pilot Robert Plath, and initially sold to crew members. Plath later commercialized them, after travelers became interested after seeing them in use by crew members, and founded

2280-408: The journey. There is normally storage space provided for hand luggage, either under seating, or in overhead lockers. Trains often have luggage racks at the ends of the carriage near the doors, or above the seats if there are compartments. On aircraft, the size and weight of hand luggage is regulated, along with the number of bags. Some airlines charge for carry-on over a certain number. Smart luggage

2337-401: The length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1) ), the unit hyperbola , and so on. The two axes divide the plane into four right angles , called quadrants . The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the first quadrant . If the coordinates of

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2394-431: The line and assigning them to two distinct real numbers (most commonly zero and one). Other points can then be uniquely assigned to numbers by linear interpolation . Equivalently, one point can be assigned to a specific real number, for instance an origin point corresponding to zero, and an oriented length along the line can be chosen as a unit, with the orientation indicating the correspondence between directions along

2451-465: The line and positive or negative numbers. Each point corresponds to its signed distance from the origin (a number with an absolute value equal to the distance and a + or − sign chosen based on direction). A geometric transformation of the line can be represented by a function of a real variable , for example translation of the line corresponds to addition, and scaling the line corresponds to multiplication. Any two Cartesian coordinate systems on

2508-414: The line can be related to each-other by a linear function (function of the form x ↦ a x + b {\displaystyle x\mapsto ax+b} ) taking a specific point's coordinate in one system to its coordinate in the other system. Choosing a coordinate system for each of two different lines establishes an affine map from one line to the other taking each point on one line to

2565-555: The most common coordinate system used in computer graphics , computer-aided geometric design and other geometry-related data processing . The adjective Cartesian refers to the French mathematician and philosopher René Descartes , who published this idea in 1637 while he was resident in the Netherlands . It was independently discovered by Pierre de Fermat , who also worked in three dimensions, although Fermat did not publish

2622-412: The orientation of the three axes, as a whole, is arbitrary. However, the orientation of the axes relative to each other should always comply with the right-hand rule , unless specifically stated otherwise. All laws of physics and math assume this right-handedness , which ensures consistency. For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for x and y , respectively. When they are,

2679-429: The origin has coordinates (0, 0, 0) , and the unit points on the three axes are (1, 0, 0) , (0, 1, 0) , and (0, 0, 1) . Standard names for the coordinates in the three axes are abscissa , ordinate and applicate . The coordinates are often denoted by the letters x , y , and z . The axes may then be referred to as the x -axis, y -axis, and z -axis, respectively. Then the coordinate planes can be referred to as

2736-407: The original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values. A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane . In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to

2793-520: The plane with Cartesian coordinates ( x 1 , y 1 ) {\displaystyle (x_{1},y_{1})} and ( x 2 , y 2 ) {\displaystyle (x_{2},y_{2})} is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}.} This

2850-446: The plane, and the spherical and cylindrical coordinates for three-dimensional space. An affine line with a chosen Cartesian coordinate system is called a number line . Every point on the line has a real-number coordinate, and every real number represents some point on the line. There are two degrees of freedom in the choice of Cartesian coordinate system for a line, which can be specified by choosing two distinct points along

2907-468: The point (0, 0, 1) ; a convention that is commonly called the right-hand rule . Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers ; that is, with the Cartesian product R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , where R {\displaystyle \mathbb {R} }

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2964-423: The point on the other line with the same coordinate. A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system ) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning each axis into

3021-401: The point where the axes meet is called the origin of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in (3, −10.5) . Thus the origin has coordinates (0, 0) , and the points on the positive half-axes, one unit away from the origin, have coordinates (1, 0) and (0, 1) . In mathematics, physics, and engineering,

3078-414: The rolling luggage patent, which was officially known as; United States patent 3,653,474 for “Rolling Luggage”, in 1970. Two years later in 1972 Bernard D. Sadow was given the wheeled suitcases patent, which became successful. The patent application cited the increase in air travel, and "baggage handling [having] become perhaps the single biggest difficulty encountered by an air passenger", as background of

3135-421: The signed distances from the point to n mutually perpendicular fixed hyperplanes . Cartesian coordinates are named for René Descartes , whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra and calculus . Using the Cartesian coordinate system, geometric shapes (such as curves ) can be described by equations involving

3192-560: The train of people and goods, both military and of a personal nature, which commonly followed pre-modern armies on campaign. The baggage was considered a strategic resource and guarded by a rear guard . Its loss was considered to weaken and demoralize an army, leading to rearguard attacks such as that at the Battle of Agincourt . Vertical axis In geometry , a Cartesian coordinate system ( UK : / k ɑːr ˈ t iː zj ə n / , US : / k ɑːr ˈ t iː ʒ ə n / ) in

3249-458: The word luggage originally meant inconveniently heavy baggage and comes from the verb lug and the suffix -age . Luggage carriers – light-weight wheeled carts on which luggage could be temporarily placed or that can be temporarily attached to luggage – date at least to the 1930s, such as in US patent 2,132,316 "Luggage carrier" by Anne W. Newton (filed 1937, published 1938). These were refined over

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