# Line vs Hyperplane - What's the difference?

line | hyperplane |

## In geometry terms the difference between line and hyperplane

is that line is an infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness while hyperplane is an n-dimensional generalization of a plane; an affine subspace of dimension n-1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane..

## As nouns the difference between line and hyperplane

is that line is a path through two or more points (compare ‘segment’); a continuous mark, including as made by a pen; any path, curved or straight while hyperplane is an n-dimensional generalization of a plane; an affine subspace of dimension n-1 that splits an n-dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane..

## As a verb line

is to place (objects) into a line (usually used with "up"); to form into a line; to align.

# line

## English

(wikipedia line)

### Etymology 1

From (etyl) (m), (m), from (etyl) . (cognates) Cognate with (etyl) . Influenced in (etyl) by (etyl) , from Latin (m). More at (l). The oldest sense of the word is "rope, cord, thread"; from this the senses "path", "continuous mark" were derived.

#### Noun

(en noun)
• A path through two or more points (compare ‘segment’ ); a continuous mark, including as made by a pen; any path, curved or straight.
• :
• *{{quote-book, year=1816, author=(w)
• , title= The Daemon of the World , passage=The atmosphere in flaming sparkles flew; / And where the burning wheels / Eddied above the mountain’s loftiest peak / Was traced a line of lightning.}}
• *
• *:So this was my future home, I thought!Backed by towering hills, the but faintly discernible purple line of the French boundary off to the southwest, a sky of palest Gobelin flecked with fat, fleecy little clouds, it in truth looked a dear little city; the city of one's dreams.
• *{{quote-book, year=2009, author=Jory Sherman, title=Sidewinder
• , passage=For their present position, he drew an inverted V. Then he drew a line and on either side he inscribed landmarks, ridges, passes. At the other end he drew a number of inverted Vs to represent the Arapaho village.}}
• #(label) An infinitely extending one-dimensional figure that has no curvature; one that has length but not breadth or thickness.
• # A line segment; a continuous finite segment of such a figure.
• #(label) An edge of a graph.
• #(label) A circle of latitude or of longitude, as represented on a map.
• # The equator.
• #*{{quote-book, year=1851, author=(Herman Melville), title=
• , chapter=54, passage=She [a ship called Town-Ho] was somewhere to the northward of the Line .}}
• #(label) One of the straight horizontal and parallel prolonged strokes on and between which the notes are placed.
• #(label) The horizontal path of a ball towards the batsman (see also length).
• #(label) The goal line.
• #*{{quote-news, year=2011, date=October 1, author=Clive Lindsay, work=BBC Sport
• , title= Kilmarnock 1-2 St Johnstone , passage=St Johnstone's Liam Craig had to clear off the line before Steven Anderson sent a looping header into his own net for the equaliser on 36 minutes.}}
• A rope, cord, string, or thread, of any thickness.
• *{{quote-book, year=1884, author=(Mark Twain), title=(The Adventures of Huckleberry Finn), chapter=9
• , passage=Then we hunted up a place close by to hide the canoe in, amongst the thick willows. We took some fish off of the lines and set them again, and begun to get ready for dinner.}}
• *{{quote-book, year=2007, author=Robert Newcomb, title=A March Into Darkness, page=29
• , passage=
• *{{quote-book, year=2008, author=Joshua Plunkett, Jeanne K. Hanson, title=The Complete Idiot's Guide to Trees and Shrubs, page=164
• , passage=Use fabric or nursery grade webbing around stakes and trunk, loosely tying the line to the tree about 6 inches below the point where the tree bounces back in your hand when you grab the trunk.}}
• #(label) A hose.
• Direction, path.
• :the line''' of sight;  the '''line of vision
• The wire connecting one telegraphic station with another, a telephone or internet cable between two points: a telephone or network connection.
• :
• :
• :
• A letter, a written form of communication.
• :
• A connected series of public conveyances, as a roadbed or railway track; and hence, an established arrangement for forwarding merchandise, etc.
• :
• (label) A trench or rampart, or the non-physical demarcation of the extent of the territory occupied by specified forces.
• *{{quote-book, year=1917, author=(John Masefield)
• , title= The Old Front Line , passage=This description of the old front line, as it was when the Battle of the Somme began, may some day be of use.
• The exterior limit of a figure or territory: a boundary, contour, or outline; a demarcation.
• *{{quote-book, year=1674, author=(John Milton), title=
• , volume=IV, passage=Eden'' stretch'd her Line / From ''Auran'' Eastward to the Royal Towrs / Of great ''Seleucia ,}}
• A long tape or ribbon marked with units for measuring; a tape measure.
• (label) A measuring line or cord.
• *
• *:The carpenter stretcheth out his rule; he marketh it out with a line ; he fitteth it with planes, and he marketh it out with the compass, and maketh it after the figure of a man, according to the beauty of a man; that it may remain in the house.
• That which was measured by a line, such as a field or any piece of land set apart; hence, allotted place of abode.
• *
• *:The lines are fallen unto me in pleasant places; yea, I have a goodly heritage.
• A threadlike crease or wrinkle marking the face, hand, or body; hence, a characteristic mark.
• *{{quote-book, year=1651, author=(John Cleveland), chapter=Fuscara
• , title=Minor poets of the Caroline period, editor=(George Saintsbury), year_published=1921) , passage=He tipples palmistry, and dines On all her fortune-telling lines .}}
• *{{quote-book, year=1812-1818, author=(Lord Byron), title=(w, Childe Harold's Pilgrimage)
• , passage=Though on his brow were graven lines austere.}}
• *{{quote-song, year=1975, composer=(Bob Dylan), title=(Tangled Up in Blue), album=Blood on the Tracks
• , passage=I muttered somethin' underneath my breath / She studied the lines on my face / I must admit I felt a little uneasy / When she bent down to tie the laces of my shoe / Tangled up in blue.}}
• Lineament; feature; figure (of one's body).
• *
• A more-or-less straight sequence of people, objects, etc., either arranged as a queue or column and often waiting to be processed or dealt with, or arranged abreast of one another in a row (and contrasted with a column), as in a military formation.
• :
• :
• *{{quote-book, year=1817, author=(w), title=
• , passage=A band of brothers gathering round me, made, / Although unarmed, a steadfast front
• (label) The regular infantry of an army, as distinguished from militia, guards, volunteer corps, cavalry, artillery etc.
• (senseid) A series or succession of ancestors or descendants of a given person; a family or race; compare lineage .
• *{{quote-book, author=(Geoffrey Chaucer), title=
• , passage=Of his lineage am I, and his offspring / By very line ,}}
• *{{quote-book, year=c.1604, author=(William Shakespeare), title=
• , passage=They hail'd him father to a line of kings.}}
• *
• *:Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun.
• *{{quote-book, year=1651, author=(Thomas Hobbes), title=
• , passage=[T]he rest of the history of the Old Testament derives the succession of the line' of David to the Captivity, of which ' line was to spring the restorer of the kingdom of God
• A small amount of text. Specifically:
• #A written or printed row of letters, words, numbers or other text, especially a row of words extending across a page or column, or a blank in place of such text.
• #:
• #A verse (in poetry).
• #*{{quote-book, year=1609, author=(William Shakespeare), title=
• , passage=Nay if you read this line , remember not, / The hand that writ it.}}
• #A sentence of dialogue, especially or the like.
• #:
• #:
• #*
• #A lie or exaggeration, especially one told to gain another's approval or prevent losing it.
• #:
• Course of conduct, thought, occupation, or policy; method of argument; department of industry, trade, or intellectual activity.
• *
• The official, stated position (or set of positions) of an individual or group, particularly a political or religious faction.
• :
• The products or services sold by a business, or by extension, the business itself.
• :
• :
• :
• (label) A number of shares taken by a jobber.
• A measure of length:
• #(label) A tsarist-era Russian unit of measure, approximately equal to one tenth of an English inch, used especially when measuring the calibre of firearms.
• #*{{quote-book, year=1906, title=Reports of military observers to the armies in Manchuria, page=261
• , passage=The arm of the Russian infantry is the three-line rifle, model 1891 (caliber 0.299 inch)
• #*{{quote-book, year=2013, title=The United States in the First World War: An Encyclopedia, page=561, ISBN=1135684464
• , passage=A “line” was a unit of measurement used in tsarist Russia and equal to about a tenth of an inch. The 3-line' rifle, therefore, had a bore of three ' lines , or approximately .30 caliber.}}
• #One twelfth of an inch.
• #*{{quote-book, year=1883, author=Alfred Swaine Taylor, Thomas Stevenson, title=The principles and practice of medical jurisprudence
• , passage=The cutis measures in thickness from a quarter of a line' to a '''line''' and a half (a ' line is one-twelfth of an inch).}}
• #One fortieth of an inch.
• #*{{quote-book, year=1922, title=Hearings Before the Committee on Finance, United States Senate, chapter=Statement of James Turner, Representing Universal Button Fastening Co., Detriot, Mich., page=5337
• , passage=In case any of the committee do not understand what is meant by a rate per line', I may say that buttons, being very small, are not measured by the foot or inch, but by the line, a line being one-fortieth of an inch. For example, that is a 27-' line button
• (label) Alternative name for a maxwell, a unit of magnetic flux.
• *{{quote-book, year=1898, author=Alfred Eugene Wiener, title=Practical calculation of dynamo-electric machines, page=47
• , passage=At the same time, however, for calculation in the metric system, one metre is taken as the unit for the length of the conductor, one metre per second as the unit velocity, and one line per square centimetre as the unit of field density.}}
• *{{quote-book, year=1903, author=William Richard Kelsey, title=Continuous current dynamos and motors and their control, page=39
• , passage=The density will now be only one quarter of a line per square centimetre, and therefore a unit pole placed at a distance of 2 centimetres from a similar pole, will only be acted on with a force of one quarter of a dyne,
• *{{quote-book, year=1904, author=Silvanus Phillips Thompson, title=Dynamo-electric machinery: a manual for students of electrotechniques: Volume 1, Part 1, page=74
• , passage=The Paris Congress of 1900 adopted the name gauss as that of the unit of intensity of field, one gauss'' signifying one line per square centimetre. The same Congress also named one ''line'' as one ''maxwell'', but everybody still uses the term ''line .}}
• *{{quote-book, year=1909, author=Henry Metcalf Hobart, title=Electricity: a text book designed in particular for engineering, page=58
• , passage=A magnetic flux is said to have a density of one line per square centimeter when it exerts on a unit north pole a force of one dyne.}}
• The batter’s box.
• The position in which the fencers hold their swords.
• *{{quote-book, year=1861, author=George Chapman, title=Foil Practice, with a Review of the Art of Fencing, page=12
• , passage=Thus, for example, in the line' of Quarte, the direct thrust is parried by dropping the point under the adversary's blade and circling upwards, throwing off the attack in the opposite '''line''' (that of Tierce), and upon the direct thrust in the '''line''' of Tierce, by a similar action throwing off the attack in the opposite ' line (that of Quarte).}}
• (label) Proper relative position or adjustment (of parts, not as to design or proportion, but with reference to smooth working).
• :
• A small portion or serving (of a powdery illegal drug).
• *{{quote-book, year=1998, author=Luke Davis, title=Candy
• , passage="Let's have a line'." He pulled a razor blade from his pocket and scooped out a couple of mounds. He laid out seven thick '''lines''' on a mirror. He rolled up a fifty-dollar note and snorted a ' line .}}
• *{{quote-book, year=2004, author=Burl Barer, title=Broken Doll, page=64
• , passage="Yes, we did. We both did a line', but maybe close to a half gram of crystal meth. I did a '''line''' and he did a way much bigger ' line ."}}
• *{{quote-book, year=2007, author=D. C. Fuller, title=Meth Monster: Crankin' Thru Life a Look Into the Abyss, page=474
• , passage=Snorting it was a much slower blast off and a longer less intense buzz, that was much easier to function on. A few minutes after you snort a line you can feel the niacin rush coming up your back and washing over your head,
• (label) Instruction; doctrine.
• *
• *:Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun.
• (lb) Population of cells derived from a single cell and containing the same genetic makeup.
• A catheter introduced in a vein or peripheral artery.
• ##### Synonyms
* straight line * line segment * (letter) epistle, letter, note * (row of text) row
##### Derived terms
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

#### Verb

(lin)
• (label) To place (objects) into a line (usually used with "up"); to form into a line; to align.
• (label) To place persons or things along the side of for security or defense; to strengthen by adding; to fortify.
• * {{quote-book
• , year=1599 , author= , title= , section=ii 4 , passage=Line and new repair our towns of war With men of courage and with means defendant.}}
• To form a line along.
• * {{quote-book
• , year=1899 , author=Juliana Horatia Gatty Ewing , title=We and the world: a book for boys , page=19 , passage=
• * {{quote-book
• , year=1909 , title=Road Notes : Cuba , publisher=, Second Section, General Staff , page=359 , section=No. 16 , passage=The mountains which have lined the road on the left here cross it and the road makes a very sharp ascent, going over them.}}
• * {{quote-book
• , year=2009 , author=Jon Fasman , title=The Unpossessed City , passage=Knee-high garden lamps lined the path; Jim was careful to stay in their pools. Assuming he was being watched, the last thing he wanted to do was give them any reason to chase after him in the dark.}}
• (label) To mark with a line or lines, to cover with lines.
• To represent by lines; to delineate; to portray.
• * {{quote-book
• , year=1598 , author= , title= , section=iii 2 , passage=All the pictures fairest lined Are but black to Rosalind.}}
• (label) To read or repeat line by line.
• To form or enter into a line.
• To hit a line drive; to hit a line drive which is caught for an out. Compare fly and ground.
• To track (wild bees) to their nest by following their line of flight.
• ### Etymology 2

#### Noun

(-)
• (label) Flax; linen, particularly the longer fiber of flax.
• * {{quote-book
• , year=1590 , author= , title=, Book V, Canto VII, VI , chapter= , passage=And clothed all in Garments made of line .}}

#### Verb

(lin)
• (label) To cover the inner surface of (something), originally especially with linen.
• * {{quote-book
• , year=1963 , author=(Margery Allingham) , title=(The China Governess) , chapter=6 citation , passage=Even in an era when individuality in dress is a cult, his clothes were noticeable. He was wearing a hard hat of the low round kind favoured by hunting men, and with it a black duffle-coat lined with white.}}
• To reinforce (the back of a book) with glue and glued scrap material such as fabric or paper.
• * {{quote-book
• , year=1891 , title=English mechanics and the world of science , volume=52 , page=306 , passage=
• * {{quote-book
• , year=1895 , volume=VIII , title=The British Printer , page=94 , passage=Then again line the back, again bringing the paper a little further in than the second lining, and repeat the operation according to what you think the weight and size of the book demands in extra strength,
• (label) To fill or supply (something), as a purse with money.
• * {{quote-book
• , title=Carew's Survey of Cornwall , page=34 , author= , editor=Thomas Tonkin , year=1602 , year_published=1811 , passage=because the charge amounteth mostly very high for any one man's purse, except lined beyond ordinary, to reach unto citation
##### Derived terms
(terms derived from the verb "line") * line one's pockets

### Etymology 3

.

#### Verb

(lin)
• to copulate with, to impregnate.
• * {{quote-book
• , year=1825 , author=A Lawson , title=The Modern Farrier , passage=A bitch lined by a mangy dog is very liable to produce mangy puppies, and the progeny of a mangy bitch is certain to become affected some time or other.}}
• * {{quote-book
• , year=1855 , author=William Youatt , title=The Dog , passage=Pliny states that the inhabitants of India take pleasure in having their dog bitches lined by the wild tigers, and to facilitate this union, they are in the habit of tieing them when in heat out in the woods, so that the male tigers may visit them.}}
• * 1868 September, The Country Gentleman's Magazine , page 292:
• Bedlamite was a black dog, and although it may be safely asserted that he lined upwards of 100 bitches of all colours, red, white, and blue, all his produce were black.

### References

(Webster 1913)

*

### Anagrams

* * * * 200 English basic words ----

# hyperplane

## English

### Noun

(en noun)
• (geometry) An n''-dimensional generalization of a plane; an affine subspace of dimension ''n-1'' that splits an ''n -dimensional space. (In a one-dimensional space, it is a point; in two-dimensional space it is a line; in three-dimensional space, it is an ordinary plane.)