perpendicular
American Heritage Dictionary:
Top
per·pen·dic·u·lar
(pûr'pən-dĭk'yə-lər) 
adj.
In a perpendicular position.
n.
perpendicularly per'pen·dic'u·lar·ly adv.
adj.
- Mathematics. Intersecting at or forming right angles.
- Being at right angles to the horizontal; vertical. See synonyms at vertical.
- often Perpendicular Of or relating to a style of English Gothic architecture of the 14th and 15th centuries, characterized by emphasis of the vertical element.
In a perpendicular position.
n.
- Mathematics. A line or plane perpendicular to a given line or plane.
- A perpendicular position.
- A device, such as a plumb line, used in marking the vertical from a given point.
- A vertical or nearly vertical line or plane.
[Middle English perpendiculer, from Old French, from Latin perpendiculāris, from perpendiculum, plumb line, from perpendere, to weigh carefully : per-, per- + pendere, to weigh.]
perpendicularity per'pen·dic'u·lar'i·ty (-lăr'ĭ-tē) n.perpendicularly per'pen·dic'u·lar·ly adv.
Roget's Thesaurus:
Top
perpendicular
adjective
- At right angles to the horizon or to level ground: plumb, upright, vertical. See horizontal/vertical/change of position.
Antonyms by Answers.com:
Top
perpendicular
adj
Definition: at right angles to; standing
Antonyms: horizontal, level
Oxford Dictionary of Architecture & Landscaping:
Top
Perpendicular
Third and latest of the English Gothic architectural styles, also known as Third Pointed or Rectilinear, it followed from the previous Decorated or Second Pointed style. The Perp. style first emerged in designs of c.1332 for the chapter-house and cloisters of old St Paul's Cathedral, London (destroyed), by William de Ramsey: key Perp. details, including mullions extending to the soffits of window-arches; extensive use of the bowtell; developed employment of the double-ogee; quatrefoils set in squares; bases with circular rolls, bells, and cushions over octagonal sub-bases of bell form; four-centred arches with flattened upper arcs; and square-framed arches with cusped blind spandrels were all evident. So the Perp. style emerged in the first half of C14 in London, and was further developed at Gloucester Cathedral, where the chancel (c.1337–57) displays many of its attributes, including the panel-like effect created by vertical and horizontal elements. An English style, it has no Continental, Irish, or Scottish equivalent, and survived for more than three centuries (the fan-vaulted hall staircase at Christ Church, Oxford, is c.1640). It was the first of the Gothic styles to be revived in C18.
Perp. is immediately recognizable by its pronounced verticals and horizontals in blind panels covering wall surfaces and in tracery (where the transoms are often ornamented with miniature battlements, and mullions rise straight up to the soffits of window-openings). Apertures gradually acquired flatter tops, with arches of the four-centred type. Vaults evolved from the complicated varieties involving liernes into the fan-vaults first found at the Chapter House of Hereford Cathedral (destroyed 1769) and the Cloisters of Gloucester Cathedral (both second half of C14), and developing into the spectacular fan-vaulting of King's College Chapel, Cambridge (early C16), and the Lady Chapel (or Chapel of King Henry VII (reigned 1485–1509)) at Westminster Abbey (1503–19). Rectangular mouldings framing door-or window-openings formed spandrels (often ornamented) reinforcing the controlled panel-like appearance: those hood-mouldings terminated in carved label-stops. Indeed, the panel motif is one of the most recognizable features of the style, each framed panel having an arched top, often cusped, and is repeated in rows in tracery and over the walls as blind panels. Windows got larger, composed of many lights (repeating the panel-like forms), and often filled the entire wall between buttresses.
The Perp. style is commonly found in parish-churches, especially in East Anglia, the Cotswolds, and Somerset, where great wealth was created by the wool trade. Clerestoreys were added to existing churches, and they often were vast, airy, and light: as naves were increased in height to accommodate ranges of large Perp. windows in their clerestoreys, roofs were flattened, and disappeared behind crenellated decorative parapets. In East Anglia, especially, chancels were not distinctly compartmented, being part of the main volume of the church, but demarcated by means of elaborate timber screens, often sumptuously decorated and coloured. Mouldings tended to become mechanical, and foliage less deeply cut than previously: a common moulding was the grapevine or trail, often found on screens and canopies.
The use of hood-mouldings, the flattening of roofs and arches, the adoption of wide-spread crenellations, and the elaboration of lierne- and later fan-vaulting gave the Perp. style its predominant flavour. Perp. architecture from the end of C15 to the beginnings of the Elizabethan style is often called Tudor, and frequently featured brick walls ornamented with diaper-work, very flattened arches, and prominent hood-mouldings. The Tudor style was revived in C19, often for schools, work-houses, and collegiate buildings.
Typical external (left) and internal (right) bay in the Perpendicular style (Church of Holy Trinity, Long Melford, Suffolk).
Typical external (left) and internal (right) bay in the Perpendicular style (Church of Holy Trinity, Long Melford, Suffolk).
Bibliography
- Harvey (1978)
- W. Papworth (1852)
- J. Parker (1850)
The full bibliography for this book is available to download as a pdf file.
Download the bibliography for A Dictionary of Architecture and Landscape Architecture (PDF: 1.2MB)
Word Tutor:
Top
perpendicular
IN BRIEF: At or forming a right angle to or with an intersecting line or plane. Also: Upright or vertical; pointing to the zenith.
The wall should be perpendicular to the floor.
LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!
Random House Word Menu:
Top
categories related to 'perpendicular'
- Geometric Shapes and Mathematically Defined Forms - perpendicular: (adj) at right angle to plane or line
- Relative Positions - perpendicular: (adj) exactly at right angles to a flat surface or plane
Bradford's Crossword Solver's Dictionary:
Top
perpendicular
See crossword solutions for the clue Perpendicular.
Wikipedia on Answers.com:
Top
Perpendicular
 |
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2011) |
For other uses, see Perpendicular (disambiguation).
In geometry, two lines or planes (or a line and a plane) are considered perpendicular (or orthogonal) to each other if they form congruent adjacent angles (a T-shape). The term may be used as a noun or adjective. Thus, as illustrated, the line AB is the perpendicular to CD through the point B.
By definition, a line is infinitely long, and strictly speaking AB and CD in this example represent line segments of two infinitely long lines. Hence the line segment AB does not have to intersect line segment CD to be considered perpendicular lines, because if the line segments are extended out to infinity, they would still form congruent adjacent angles.
If a line is perpendicular to another as shown, all of the angles created by their intersection are called right angles (right angles measure π/2 radians, or 90°). Conversely, any lines that meet to form right angles are perpendicular.
In a coordinate plane, perpendicular lines have opposite reciprocal slopes, which means that the product of their slopes is -1. A horizontal line has slope equal to zero while the slope of a vertical line is described as undefined or sometimes ±infinity. Two lines that are perpendicular would be denoted as AB
CD.
|
Contents
|
Construction of the perpendicular
To make the perpendicular to the line AB through the point P using compass and straightedge, proceed as follows (see figure):
- Step 1 (red): construct a circle with center at P to create points A' and B' on the line AB, which are equidistant from P.
- Step 2 (green): construct circles centered at A' and B' having equal radius. Let Q and R be the points of intersection of these two circles.
- Step 3 (blue): connect Q and R to construct the desired perpendicular PQ.
To prove that the PQ is perpendicular to AB, use the SSS congruence theorem for ' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS congruence theorem for triangles OPA' and OPB' to conclude that angles POA and POB are equal.
In relationship to parallel lines
If two lines (a and b) are both perpendicular to a third line (c), all of the angles formed along the third line are right angles. Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate. Conversely, if one line is perpendicular to a second line, it is also perpendicular to any line parallel to that second line.
In the figure at the right, all of the orange-shaded angles are congruent to each other and all of the green-shaded angles are congruent to each other, because vertical angles are congruent and alternate interior angles formed by a transversal cutting parallel lines are congruent. Therefore, if lines a and b are parallel, any of the following conclusions leads to all of the others:
- One of the angles in the diagram is a right angle.
- One of the orange-shaded angles is congruent to one of the green-shaded angles.
- Line 'c' is perpendicular to line 'a'.
- Line 'c' is perpendicular to line 'b'.
Perpendicular symbol
The perpendicular symbol is . For example, 
indicates that line AB is perpendicular to line CD.
In the Unicode character set, the perpendicular sign has the codepoint U+27C2 and is part of the Miscellaneous Mathematical Symbols-A range. It looks similar to the up tack symbol (U+22A5).
Graph of functions
In 2-dimension plane, right angles can be formed by two intersected lines which the product of their slopes equals to −1. More precisely, defining two linear functions: y1 = a1x + b1 and y2 = a2x + b2, the graph of the functions will be perpendicular and will make four right angles where the lines intersect if and only if a1a2 = −1. However, this method cannot be used if the slope is zero or infinity (the line parallels to an axis).o
For another method, let the two linear functions: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. The lines will be perpendicular if and only if a1a2 + b1b2 = 0. This method is simplified from the dot product (or generally, inner product) of vectors. In particular, two vectors are considered orthogonal if their inner product is zero.
See also
External links
- Definition: perpendicular With interactive animation
- How to draw a perpendicular bisector of a line with compass and straight edge Animated demonstration
- How to draw a perpendicular at the endpoint of a ray with compass and straight edge Animated demonstration
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
Top
Perpendicular
Dansk (Danish)
adj. - vinkelret
n. - lodret linje, lodret flade
Nederlands (Dutch)
loodrecht, verticaal, zeer steil, rechtop, betreffende/ bevattende uiteenlopende types, loodlijn, waterpas, stijl in Engelse gotiek
Français (French)
adj. - perpendiculaire
n. - perpendiculaire
Deutsch (German)
adj. - senkrecht, aufrecht
n. - Senkrechte, Lot
Ελληνική (Greek)
adj. - κατακόρυφος, κάθετος
n. - κάθετος
Italiano (Italian)
perpendicolare
Português (Portuguese)
adj. - perpendicular (Geom.), vertical
n. - perpendicular (f), vertical (f), prumo (m)
Русский (Russian)
перпендикулярный, перпендикуляр
Español (Spanish)
adj. - perpendicular, vertical
n. - línea o plano perpendicular, comida que se toma de pie
Svenska (Swedish)
adj. - lodrät, vertikal, upprätt (skämts.)
n. - normal (geom.), lodlina, lodrätt plan, upprätt ställning
中文（简体）(Chinese (Simplified))
垂直的, 直立的, 垂直线, 垂直的位置
中文（繁體）(Chinese (Traditional))
adj. - 垂直的, 直立的
n. - 垂直線, 垂直的位置
한국어 (Korean)
adj. - 수직의, 깎아 세운 듯한
n. - 수직선, 수직, 수직식 건축
日本語 (Japanese)
n. - 垂線, 垂直面, 垂直の位置, 垂直
adj. - 垂直の, 直角の, 直立した
العربيه (Arabic)
(صفه) عموددي : خط مستقيم, متعامد (الاسم) قائم الإنحدار, شديد التحدر
עברית (Hebrew)
adj. - מאונך, אנכי, ניצב
n. - אנך, ניצב
If you are unable to view some languages clearly, click here.
Post a question - any question - to the WikiAnswers community:
Copyrights:
American Heritage Dictionary
The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.
Read more
Roget's Thesaurus
Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 byHoughton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.
Read more
Oxford Dictionary of Architecture & Landscaping
A Dictionary of Architecture and Landscape Architecture. Copyright © 1999, 2006 by Oxford University Press. All rights reserved.
Read more
Word Tutor
Copyright © 2004-present by eSpindle Learning, a 501(c) nonprofit organization. All rights reserved.
eSpindle provides personalized spelling and vocabulary tutoring online; sign up free. Read more
eSpindle provides personalized spelling and vocabulary tutoring online; sign up free. Read more
Random House Word Menu
© 2010 Write Brothers Inc. Word Menu is a registered trademark of the Estate of Stephen Glazier.
Write Brothers Inc.
All rights reserved.
Read more
Bradford's Crossword Solver's Dictionary
Collins Bradford's Crossword Solver's Dictionary © Anne Bradford, 1986, 1993, 1997, 2000, 2003, 2005, 2008
HarperCollins Publishers
All rights reserved.
Read more
Wikipedia on Answers.com
This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article Perpendicular.
Read more
