About four sided mathematical shapes Infobox Polygon name Quadrilateral image Six Quadrilaterals.svg ... Area of a convex quadrilateral see below angle 90 for square In Euclidean geometry Euclidean plane geometry , a quadrilateral is a polygon with four sides or edges and four vertices or corners. Sometimes ... with pentagon 5 sided , hexagon 6 sided and so on. The word quadrilateral is made of the words quad meaning four and lateral meaning of sides . The origin of the word quadrilateral is from the two Latin ... angle interior angles of a simple quadrilateral add up to 360 degrees of arc . This is a special case of the n gon interior angle sum formula n 2 180 . In a crossed quadrilateral, the interior angles ... parallelograms File Euler diagram of quadrilateral types.svg thumb 300px Euler diagram of some ... is a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides ... . Square geometry Square regular quadrilateral all four sides are of equal length equilateral ... length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle four equal .... It is common, especially in the discussions on plane tessellations , to refer to the concave quadrilateral ... shape. Orthodiagonal quadrilateral the diagonals cross at right angle s. Trapezoid Trapezium British ..., and that the diagonals are of equal length. An alternative definition is a quadrilateral with an axis ... this would be called an irregular quadrilateral, and was once called a trapezoid . Cyclic quadrilateral the four vertices lie on a circumscribed circle. A quadrilateral is cyclic if and only if opposite angles sum to 180 . Tangential quadrilateral the four sides are tangents to an inscribed circle. Another term for a tangential polygon is inscriptible . Bicentric quadrilateral both cyclic and tangential. Ex tangential quadrilateral the four extensions of the sides are tangent to an excircle. Image Quadrilaterals.svg More quadrilaterals An equilic quadrilateral has two opposite equal sides that, when ... more details
Wiktionarypar quadrilateral The word quadrilateral can refer to Quadrilateral , in geometry, a polygon with 4 sides Complete quadrilateral , in projective geometry, a configuration with 4 lines and 6 points Chicago Lambeth Quadrilateral , a four point statement of fundamental doctrine, in the Anglican Communion Wesleyan Quadrilateral , the four sources of doctrine in the Methodist Church In history and geography Quadrilatero , in the Revolutions of 1848, in the Italian states an area within the group of fortresses at Mantua, Verona, Peschiera and Legnago In the Battle of the Somme in World War I, the Quadrilateral was a German redoubt near Ginchy Southern Dobruja , which has passed from Bulgaria to Romania in 1913, and back to Bulgaria in World War II Golden Quadrilateral , a network of highways in India Golden Quadrilateral Indian Railways Quadrilateral Security Dialogue , a strategic alliance of the United States, Japan, Australia and India within Asia. See also Quadriliteral disambig pl Czworobok lmo Quadril ter ... more details
Image Lambert quadrilateral.svg thumb right A Lambert quadrilateral In geometry , a Lambert quadrilateral , ref the alternate name Ibn al Haytham&ndash Lambert quadrilateral , has been suggested in Boris Abramovich Rozenfel d 1988 , A History of Non Euclidean Geometry Evolution of the Concept of a Geometric Space , p. 65. Springer, ISBN 0387964584, in honor of Ibn al Haytham ref named after Johann Heinrich Lambert , is a quadrilateral three of whose angles are right angles. Historically, the fourth angle of a Lambert quadrilateral was of considerable interest since if it could be shown to be a right angle, then the Euclidean parallel postulate could be proved as a theorem. It is now known that the type of the fourth angle depends upon the geometry in which the quadrilateral lives. In hyperbolic geometry the fourth angle is Acute angle acute , in Euclidean geometry it is a right angle and in elliptic geometry it is an obtuse angle . A Lambert quadrilateral can be constructed from a Saccheri quadrilateral by joining the midpoints of the base and summit of the Saccheri quadrilateral. This line segment is perpendicular to both the base and summit and so either half of the Saccheri quadrilateral is a Lambert quadrilateral. See also Saccheri quadrilateral Non Euclidean geometry Hyperbolic geometry Elliptic geometry Notes Reflist References George E. Martin, The Foundations of Geometry and the Non Euclidean Plane , Springer Verlag, 1975 M. J. Greenberg, Euclidean and Non Euclidean Geometries Development and History , 4th edition, W. H. Freeman, 2008. Category Hyperbolic geometry geometry stub ar ru ... more details
File Orthodiagonal quadrilateral.svg thumb 240px An orthodiagonal quadrilateral. According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral ... geometry , an orthodiagonal quadrilateral is a quadrilateral in which the diagonal s cross at right ... quadrilateral in which one diagonal is a line of symmetry. The kites are exactly the orthodiagonal ... are the tangential quadrilateral tangential orthodiagonal quadrilaterals. ref citation last Josefsson ... lengths and tangency chords of a tangential quadrilateral url http forumgeom.fau.edu FG2010volume10 FG201013.pdf volume 10 year 2010 . ref A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides that is, an orthodiagonal quadrilateral that is also a parallelogram . A square geometry ... quadrilateral, the sum of the squares of two opposite sides equals that of the other two opposite sides ..., citation last Douglas first W. title The area of a quadrilateral journal Mathematical Gazette volume ... of the four squared distances from the quadrilateral s vertices to the point where the diagonals cross. Conversely, any quadrilateral in which math 1 a sup 2 sup c sup 2 sup b sup 2 sup d sup 2 sup ... quadrilateral equals one half the product of the lengths of the diagonals p, q ref Harries, J. Area of a quadrilateral, Mathematical Gazette 86, July 2002, 310 311. ref math K frac p cdot q 2 . math The orthodiagonal quadrilateral has the biggest area of all convex quadrilaterals with given ... approaching zero as the acute angle approaches zero . In an orthodiagonal quadrilateral the two ... Court rp p.136 If Square geometry square s are erected outward on the sides of a convex quadrilateral , then their Centre geometry centre s centroid s are the vertices of an orthodiagonal quadrilateral with diagonals of equal length. The quadrilateral formed by the midpoints of the sides of an orthodiagonal quadrilateral is a rectangle . Properties of orthodiagonal quadrilaterals that are also ... more details
Image Tangential quadrilateral.svg thumb An example of a tangential quadrilateral In Euclidean geometry , a tangential quadrilateral or circumscribed quadrilateral is a convex polygon convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral. This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius ... the tangential quadrilaterals that are also orthodiagonal quadrilateral orthodiagonal . ref ... Calculations concerning the tangent lengths and tangency chords of a tangential quadrilateral url http forumgeom.fau.edu FG2010volume10 FG201013.pdf volume 10 year 2010 . ref If a quadrilateral is both tangential and cyclic quadrilateral cyclic , it is called a bicentric quadrilateral . Characterizations ... of the radii of circles within each of four triangles In a tangential quadrilateral, the four angle bisector s meet at the center of the incircle. Conversely, a convex quadrilateral in which the four ... Andreescu According to the Pitot theorem , the two pairs of opposite sides in a tangential quadrilateral add to the same total length, which equals the semiperimeter of the quadrilateral math a c b d frac a b c d 2 s. math Conversely a convex quadrilateral in which a c b d must be tangential. ref name Andreescu ref name Josefsson2 rp p.65 If opposite sides in a convex quadrilateral ABCD that is not a trapezoid ... the same as one of the equalities in Ex tangential quadrilateral Urquhart s Theorem Urquhart ... instead of differences. Another necessary and sufficient condition is that a convex quadrilateral ... of any convex quadrilateral partition the quadrilateral into four triangles. Let r sub 1 sub , r sub ... adjacent triangles then the quadrilateral is tangential if and only if math frac 1 r 1 frac ... s in the same four triangles from the diagonal intersection to the sides of the quadrilateral , then the quadrilateral ... side of the quadrilateral and the extensions of its diagonals . The quadrilateral is tangential if and only ... more details
File Bicentric quadrilateral.png thumb A bicentric quadrilateral ABCD File Bicentric kite 001.svg thumb right A right kite geometry kite File Bicentric quadrilateral 2.png thumb A bicentric quadrilateral ABCD and its contact quadrilateral WXYZ In Euclidean geometry , a bicentric quadrilateral is a convex polygon convex quadrilateral that has both an incircle and a circumcircle . This means they have all the properties of both tangential quadrilateral s and cyclic quadrilateral s. Other names are chord tangent quadrilateral ref name Dorrie D rrie, Heinrich, 100 Great Problems of Elementary Mathematics ... quadrilateral . Special cases Examples of bicentric quadrilaterals are square geometry squares ... isosceles tangential trapezoids . Characterizations A convex quadrilateral ABCD with sides a , b ... characterizations concern the points where the incircle in a tangential quadrilateral is tangent ..., then a tangential quadrilateral ABCD is also cyclic if and only if any of ref name Josefsson citation ... . ref math WY bot , XZ math That is, the contact quadrilateral WXYZ is an orthodiagonal quadrilateral ... of WX , XY , YZ , ZW respectively, then the tangential quadrilateral ABCD is also cyclic if and only if the quadrilateral EFGH is a rectangle . ref name Josefsson According to another characterization, if I is the incenter in a tangential quadrilateral where the extensions of opposite sides intersect at J and K , then the quadrilateral is also cyclic if and only if JIK is a right angle . ref name Josefsson Yet another necessary and sufficient condition is that a tangential quadrilateral ... quadrilateral WXYZ . The Newton line of a quadrilateral is the line defined by the midpoints of its diagonals. ref name Josefsson Construction There is a simple method for constructing a bicentric quadrilateral ... are the vertex geometry vertices of a bicentric quadrilateral. ref Alsina, Claudi and Nelsen, Roger ... quadrilateral ABCD , the contact quadrilateral WXYZ has perpendicular diagonal s if and only ... more details
Image Cyclic quadrilateral.svg thumb right Cyclic quadrilaterals. In Euclidean geometry , a cyclic quadrilateral is a quadrilateral whose vertex geometry vertices all lie on a single circle . This circle ... names for these quadrilaterals are chordal quadrilateral and inscribed quadrilateral . Usually the quadrilateral is assumed to be Convex and concave polygons convex , but there are also crossed ... if and only if it has two right angles. A bicentric quadrilateral is a cyclic quadrilateral that is also tangential quadrilateral tangential and an Ex tangential quadrilateral Ex bicentric quadrilateral ex bicentric quadrilateral is a cyclic quadrilateral that is also Ex tangential quadrilateral ex tangential . Characterizations A convex quadrilateral is cyclic if and only if the four perpendicular bisectors to the sides are concurrent . This common point is the circumcenter . A convex quadrilateral ... Book 3, Proposition 22 of Euclid s Elements . ref Equivalently, a convex quadrilateral is cyclic ... and sufficient condition for a convex quadrilateral ABCD to be cyclic is that an angle between a side ..., math angle ACB angle ADB. math Yet another characterization is that a convex quadrilateral ... pages 103 106 title A Condition for a Circumscriptible Quadrilateral to be Cyclic url http forumgeom.fau.edu ... frac B 2 tan frac D 2 . math Area The area K of a cyclic quadrilateral with sides a , b , c , d is given ... opposite angles are supplementary. If also nowrap d 0 , the cyclic quadrilateral becomes a triangle and the formula is reduced to Heron s formula . The cyclic quadrilateral has Maxima and minima maximal ... of a Quadrilateral , The College Mathematics Journal, Vol. 34, No. 4 Sep., 2003 , pp. 315 316 ... c , or side d . The area of a cyclic quadrilateral with successive sides a , b , c , d and angle ... of a cyclic quadrilateral as equal to the sum of the products ac and bd of opposite sides ref name ... is satisfied in a convex quadrilateral, then it is a cyclic quadrilateral. Thus Ptolemy ... more details
Image Saccheri quads.svg thumb right Saccheri quadrilaterals A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri , who used it extensively in his book Euclid vindicatus 1733 , an attempt to prove the parallel postulate using the method Reductio ad absurdum . The first known consideration of the Saccheri quadrilateral was by Omar Khayyam in the late 11th century, and it may occasionally be referred to as the Khayyam Saccheri quadrilateral. ref name Rozenfeld For a Saccheri quadrilateral ABCD, the sides AD and BC also called legs are equal in length and perpendicular to the base AB. The top CD is called the summit or upper base and the angles at C and D are called the summit angles. The advantage of using Saccheri quardrilaterals when considering the parallel postulate is that they place the mutually exclusive options in very clear terms Are the summit angles right angles, obtuse angles, or acute angles? As it turns out, when the summit angles are right angles, this quadrilateral is equivalent to the statement expounded by Euclid s fifth postulate. When they are acute, this quadrilateral leads to hyperbolic geometry , and when they are obtuse, the quadrilateral leads to elliptical geometry . Saccheri himself, however, thought that both the obtuse and acute cases could be shown to be contradictory. History Saccheri quadrilaterals were first considered by Omar Khayyam 1048 1131 in the late 11th century ... the three cases right, obtuse, and acute that the summit angles of a Saccheri quadrilateral can take ... he used the quadrilateral to prove that if three points are equidistant on the base AB and the summit ..., and ultimately flawed proof of the parallel postulate around the quadrilateral and its three cases ... curvature math 1 math , the summit math s math of a Saccheri quadrilateral can be calculated ... , page 104. ref See also Lambert quadrilateral Notes reflist References George E. Martin, The Foundations ... more details
Morefootnotes article date January 2009 Primarysources article date January 2009 The Wesleyan Quadrilateral is a methodology for Christian theology theological reflection that is credited to John Wesley , leader of the Methodism Methodist movement in the late 18th Century. The term itself was coined by 20th century United Methodist Church American Methodist Albert C. Outler in his introduction to the 1964 collection John Wesley ISBN 0 19 502810 4 . ref cite book title John Wesley last Wesley first John editor1 first Albert C. editor1 last Outler editor1 link Albert C. Outler year 1964 publisher Oxford University Press location Oxford, England , U.K. isbn 0 19 502810 4 oclc page iv ref ref cite book first W. Stephen last Gunter coauthors Ted A. Campbell, Scott J. Jones, Rebekah L. Miles and Randy L. Maddox title Wesley and the quadrilateral renewing the conversation publisher Abingdon Press ... year 2004 page 77 isbn 0 687 02373 4 oclc 58046917 ref Wesley saw the Quadrilateral not merely ... does form theology. As an astute observer of human behavior, and a pragmatist, Wesley s approach to the Quadrilateral ... of the Wesleyan Quadrilateral must be taken in balance, and none of the other three apart from scripture ... of the complexities of a secular world. Wesley s Quadrilateral is referred to in Methodism as our ... book first Donald A. D. last Thorsen title The Wesleyan quadrilateral scripture, tradition, reason ... A. Campbell, Scott J. Jones, Rebekah L. Miles and Randy L. Maddox title Wesley and the quadrilateral ... Quadrilateral in John Wesley editor Jason Gingerich publisher Wesley Center for Applied ... imported site wesleyjournal 1985 wtj 20 1.pdf title The Wesleyan Quadrilateral in the American ... Quadrilateral month January February year 2005 journal Good News Magazine accessdate 2009 ... the Wesleyan Quadrilateral journal The Arminian volume 14 issue 2 accessdate 2009 01 25 cite journal ... foursome.html title Our Formative Foursome The Wesleyan Quadrilateral and Postmodern Discipleship ... more details
The Red Quadrilateral in Romanian Patrulaterul ro u was a term used to describe the Romanian government between the 1992 and 1996 legislative elections. The Quadrilateral consisted of the Social Democratic Party Romania Democratic National Salvation Front a major party, led by Ion Iliescu , when he became President of Romania and had to leave the party, led by Adrian N stase , the nationalist Romanian National Unity Party of Gheorghe Funar and the Greater Romania Party at that time national communist of Corneliu Vadim Tudor , and the neo communist Socialist Party of Labour of Communist Romania Ceau escu era Prime Minister Ilie Verde . ref http books.google.com books?id JrWr2xnZPCkC&pg PA75&lpg PA75&dq Partidul Socialist al Muncii romania socialist&source bl&ots MCObWLSulb&sig mRfZwpUdLxgxksxvDDEAYruXdGw&hl en&ei x0poSq2PGMjdsgbh PCFBw&sa X&oi book result&ct result&resnum 8 ref The coalition supported President Ion Iliescu and Prime Minister Nicolae V c roiu . See also V c roiu I Cabinet . During the last year, Vadim s party officially left the coalition but continued to support it in the Parliament. Funar s and Verde parties did not pass the threshold in 1996, while the other two parties joined the opposition. Notes reflist Category Political history of Romania Category Defunct political parties in Romania ro Patrulaterul ro u ... more details
Use mdy dates date August 2010 Infobox road country IND name Golden Quadrilateral map Golden Quadrilateral.svg map notes Highway map of India with the Golden Quadrilateral highlighted in solid blue color ... Highway 5 India NH 5 File HIghway Chennai Bangalore.jpg right thumb 250px A section of the Golden Quadrilateral ... section of India s 4 lane Golden Quadrilateral highway File NH5 highway scenic drive India.jpg thumb ... thumb NH76 Delhi Mumbai section of India s GQ highway The Golden Quadrilateral is a highway network ... , Mumbai , Chennai and Kolkata , thus forming a quadrilateral of sorts. Four other top ten metropolises ... lane GQ highway network as complete. ref cite web title Govt declares Golden Quadrilateral complete ... Golden Quadrilateral complete 896873 ref ref name nhai progress cite web url http www.nhai.org gqmain ... and cultural centers of India. The vast majority of the Golden Quadrilateral GQ is not Limited ... visibility signs are in use. India s government had initially estimated that the Golden Quadrilateral ... web title Contractors take the sheen off Golden Quadrilateral publisher The Financial Express date 3 August 2011 url http www.financialexpress.com news contractors take the sheen off golden quadrilateral ... fe full story.php?content id 100459 title Golden Quadrilateral still has miles ... activity in the GQ project. The fastest team to circumnavigate the entire Golden Quadrilateral ... National Highway India National Highways are used in the Golden Quadrilateral. The four legs use the following ... NH 5 Balasore Chennai Important cities connected by Golden Quadrilateral highway class wikitable ... news Govt declares Golden Quadrilateral complete 896873 Govt. of India declares Golden Quadrilateral ... Quadrilateral in each State The completed Golden Quadrilateral will pass through 13 States ... Development Project North South and East West Corridor Transport in India Golden Quadrilateral Indian ... http www.financialexpress.com fe full story.php?content id 100459 Golden Quadrilateral still has ... more details
Orphan date February 2009 The Quadrilateral group or the Quad is an informal group which includes the trade minister s of the European Commission , the United States , Japan and Canada . It was first suggested during a private meeting during the 7th G7 summit in July 1981. Initially, a trilateral group was proposed excluding Canada because of tensions between the two North American countries at the time but eventually, the Canadian government successfully lobbied to be included. ref name cohn cite book last Cohn first Theodore H. title Governing Global Trade International institutions in conflict and convergence publisher Ashgate Publishing Limited location Hampshire, England year 2002 isbn 0754615936 ref The European Commission has avoided formalizing the group because of resistance from certain European Union members, particularly France , who resent their lack of direct involvement. ref name cohn Quadrilateral Meetings of Trade Ministers class wikitable Location Dates ref name cohn Key Biscayne, Florida , USA 15 16 January 1982 Chateau d Esclimont , France 12 13 May 1982 Tokyo , Japan 11 February 1983 Brussels , Belgium 29 April 1983 London , UK 16 17 July 1983 Ottawa, Ontario , Canada 26 27 September 1983 Islamorada, Florida , USA 2 4 February 1984 Erbach Im Reingau , Germany 28 30 June 1984 Kyoto , Japan 9 11 February 1985 Oba, Ontario , Canada 11 14 July 1985 San Diego, California , USA 16 19 January 1986 Sinta , Portugal 4 7 September 1986 Kashikojima , Japan 24 26 April 1987 Quadra Island, British Columbia , Canada 15 17 April 1988 Brainerd, Minnesota , USA 22 24 June 1988 The Hague , Netherlands 2 4 June 1989 Hakonemachi , Japan 12 14 November 1989 Napa, California , USA 2 4 May 1990 St. John s, Newfoundland , Canada 11 13 October 1990 Angers , France 12 14 September 1991 Fukushima, Fukushima Fukushima , Japan 24 26 April 1992 Cambridge, Ontario , Canada 16 18 October 1992 Toronto, Ontario , Canada 12 14 May 1993 Tokyo, Japan 23 24 June 1993 Los Angeles, California ... more details
File Ex tangential quadrilateral.png thumb An ex tangential quadrilateral ABCD In Euclidean geometry , an ex tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral. ref name Radic Radic, Mirko Kaliman, Zoran and Kadum, Vladimir, A condition that a tangential quadrilateral is also a chordal one , Mathematical Communications , 12 2007 pp. 33 52. ref It has also been called an exscriptible quadrilateral . ref Bogomolny, Alexander, Inscriptible and Exscriptible Quadrilaterals , Interactive Mathematics Miscellany and Puzzles , http www.cut the knot.org Curriculum Geometry Pitot.shtml . Accessed 2011 08 18. ref The circle ... tangential quadrilateral is closely related to the tangential quadrilateral where the four sides are tangent .... Characterizations A convex quadrilateral with sides a, b, c, d is ex tangential if and only if the sum ... to the Pitot theorem for tangential quadrilateral s, where the sums of opposite sides are equal for the two pairs of opposite sides. Urquhart s Theorem If opposite sides in a convex quadrilateral ... and sufficient condition for a quadrilateral to be ex tangential. Area An ex tangential quadrilateral ... Note that this is the same formula as the one for the area of a tangential quadrilateral and it is also derived from Bretschneider s formula in the same way. Ex bicentric quadrilateral If an ex tangential quadrilateral also has a circumcircle , it is called an ex bicentric quadrilateral . ref name Radic ... sqrt abcd math which is the same as for a bicentric quadrilateral . If x is the distance between the circumcenter ... as Bicentric quadrilateral Fuss theorem and Carlitz identity Fuss theorem for a bicentric quadrilateral ... bicentric quadrilateral compared to the bicentric. Hence, for the ex bicentric we have ref name Radic ... also Bicentric quadrilateral Cyclic quadrilateral Kite geometry Kite Orthodiagonal quadrilateral Rhombus Tangential quadrilateral Complete quadrangle References reflist Category Quadrilaterals Category ... more details
Image wrhunt ton.jpg thumb 175px William Reed Huntington s essay was the basis of the Quadrilateral. Anglicanism The Chicago Lambeth Quadrilateral , frequently referred to as the Lambeth Quadrilateral or the Lambeth Chicago Quadrilateral , is a four point articulation of Anglican identity, often cited as encapsulating the fundamentals of the Communion s doctrine and as a reference point for ecumenism ecumenical discussion with other Christian denominations. The four points are The Bible Holy Scripture s, as containing all things necessary to salvation The Creeds specifically, the Apostles Creed Apostles and Nicene Creed Nicene Creeds , as the sufficient statement of Christian faith The Anglican sacraments Sacraments of Baptism and Holy Communion The historic episcopate , locally adapted. The Quadrilateral had its genesis in an 1870 essay by an American Episcopal Church in the United States Episcopal priest, William Reed Huntington . Huntington s purpose in proposing these four elements was to establish a basis on which approach may be by God s blessing, made toward Home Reunion, that is, with the Roman Catholic Church Roman Catholic and Orthodox Church Orthodox Churches. American House of Bishops resolution The four points found their way into a resolution of the House of Bishops ... needs of the nations and peoples called of God into the Unity of His Church. Significance of the Quadrilateral ... the British Empire, marked in pink, in the late 19th century The Quadrilateral has had a significant ... could open the door to challenging the Church s episcopal tradition of apostolic succession . The Quadrilateral in ecumenical dialogue The Chicago Lambeth Quadrilateral has also been important to ecumenical ... to the ecumenical efforts of the Chicago Lambeth Quadrilateral. The Quadrilateral has also proved a stumbling ... of essays about the Quadrilateral Category Anglican theology and doctrine Category Episcopacy in Anglicanism ... de Lambeth Quadrilateral fr Quadrilat re de Chicago Lambeth zh ... more details
Infobox Organization name Quadrilateral Security Dialogue br small Quadrilateral small image Quadrilateral.jpg ... Minister Shinzo Abe intended for the Quadrilateral to establish an Asian Arc of Democracy. type ... United States of America , Japan , Australia , India formation May 2007 The Quadrilateral Security ... to all members. The Quadrilateral was temporarily disrupted by the departure of Australia during ... to a Quadrilateral security arrangement isolating China. India s increased military cooperation with the U.S. ... military exercises in the ensuing years before the development of a Quadrilateral dialogue, interpreted ... Asia. ref Indian political commentator Brahma Chellaney referred to the emerging Quadrilateral ... Vice President Dick Cheney into a Quadrilateral by drawing India into joint naval exercises ... dilemmas in PM s China high wire act. Sunday Age , 5 April 2009. ref Creation of the Quadrilateral ... published by the BBS Monitoring South Asia . ref The Quadrilateral was supposed to establish an Asian ... the Shanghai Cooperation Organisation , the Quadrilateral is viewed as an Asian NATO Daniel Twining ... members of the Quadrilateral before any formal convention of its members. ref Nicholson, Brendan. China ... Prime Minister John Howard participated with other members in the inaugural meeting of the Quadrilateral ... with Australia. ref name Chellaney Though the Quadrilateral initiative of the Bush Administration ... India pact signed following the creation of the Quadrilateral, stating, There was mention of China ... called contain China effort, after being asked about the Quadrilateral. ref PM says India not part ... Australian ambivalence over the Quadrilateral Fears over Chinese military spending and missile capacities ... the Quadrilateral however caused uneasiness within Australia even before the agreements were initiated ... by Rudd, Australia unilaterally departs from the Quadrilateral Following his nomination as Australian ... politician Stephen Smith in which Australia unilaterally announced its departure from the Quadrilateral ... more details
The word trapezium has several meanings Outside the US a trapezoid quadrilateral with one pair of parallel sides a shape known in the US as a trapezoid . In the US a quadrilateral with no parallel sides a shape known elsewhere as a general irregular quadrilateral . Trapezium bone , a bone in the wrist Trapezium astronomy , a group of stars in the Orion Nebula Trapezium play Trapezium play , a play by Henry Rathvon disambig ast Trapezoide ca Trapezoide es Trapezoide eu Trapezoide ... more details
wiktionary rhombic Rhombic may refer to Rhombus , a quadrilateral whose four sides all have the same length often called a diamond Rhombic antenna , a broadband directional antenna most commonly used on shortwave frequencies disambiguation ... more details
In geometry , the Japanese theorem states that the centers of the incircle s of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Triangulating an arbitrary concyclic quadrilateral by its diagonals yields four overlapping triangles each diagonal creates two triangles . The centers of the incircles of those triangles form a rectangle. Image Japanese theorem 2.svg center 600px Specifically, let math square ABCD math be an arbitrary concyclic quadrilateral and let be math M 1,M 2,M 3,M 4 math the incenters of the triangles math triangle ABD, triangle ABC, triangle BCD, triangle ACD math . Then the quadrilateral formed by math M 1,M 2,M 3,M 4 math is a rectangle. Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons . To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. The quadrilateral case immediately proves the general case by induction on the set of triangulating partitions of a general polygon. See also Carnot s theorem Sangaku Wasan References http www.math cs.cmsu.edu mjms 2006.2 mangho999.ps In Search of the Japanese Theorem http www.cut the knot.org proofs jap.shtml Japanese Theorem at Cut the Knot http www.gogeometry.com sangaku2.html Japanese theorem, interactive proof with animation Category Euclidean plane geometry Category Theorems in geometry Category Japanese mathematics ar de Japanischer Satz f r Sehnenvierecke fr Th or me japonais pour les quadrilat res inscriptibles nl Japanse stelling voor koordenvierhoeken uk ... more details
In geometry , a set mathematics set of point geometry points is said to be concyclic or cocyclic if they lie on a common circle . Image Concyclic.svg thumb right 250px right Concyclic points, showing that the perpendicular bisectors of pairs are Concurrent lines concurrent Image Four concyclic points.png thumb right 250px right Four concyclic points showing that angles math alpha math are the same. Points are the vertices of a cyclic quadrilateral A circumscribed circle circle can be drawn around any triangle . A quadrilateral that can be inscribed inside a circle is said to be a cyclic quadrilateral . In general the centre O of a circle on which points P and Q lie must be such that OP and OQ are equal distances. Therefore O must lie on the perpendicular bisector of the line segment PQ . For n distinct points there are n n &minus 1 2 such lines to draw, and the concyclic condition is that they all meet in a single point. A quadrilateral in which the four vertices are concyclic is called a cyclic quadrilateral . More generally, a polygon in which all vertices are concyclic is called a cyclic polygon . Three line mathematics noncollinear points A , B , and C are concyclic to a single circle. Four different points A , B , C , and D are cyclic if and only if see diagram math alpha equiv angle CAD angle CBD. , math This condition is equivalent to the condition that opposite angles in the quadrilateral be supplementary. Four points in the complex plane are either concyclic or collinear if and only if their cross ratio is real number real . See also Collinear points Lester s theorem External links MathWorld title Concyclic urlname Concyclic http demonstrations.wolfram.com FourConcyclicPoints Four Concyclic Points by Michael Schreiber, The Wolfram Demonstrations Project . Category Elementary geometry Elementary geometry stub ar es Puntos coc clicos sl Sokro ne to ke fr Cocyclique ... more details
The Posterior humeral circumflex vessels or Posterior circumflex humeral vessels are the Posterior humeral circumflex artery and the Posterior humeral circumflex vein which run through the Quadrangular space Quadrangular or Quadrilateral space with the Axillary nerve . Category Upper limb anatomy anatomy stub cardiovascular stub ... more details
of the Quadrilateral Special line segments tangent lengths e , f , g , h as ref name Josefsson citation ... the tangent lengths and tangency chords of a tangential quadrilateral url http forumgeom.fau.edu ... trapezoid. The inradius can also be expressed in terms of the Quadrilateral Special line segments ... trapezoid is cyclic quadrilateral cyclic , this means that an isosceles tangential trapezoid is a bicentric quadrilateral . That is, it has both an incircle and a circumcircle . If the bases are a and b ... Bicentric quadrilateral Cyclic quadrilateral Ex tangential quadrilateral Isosceles trapezoid Rhombus Square Tangential quadrilateral Trapezoid References reflist Category Quadrilaterals Category Geometry ... more details
In Euclidean geometry , Brahmagupta s formula finds the area of any quadrilateral given the lengths of the sides and some of the angles. In its most common form, it yields the area of quadrilaterals that can be inscribed in a circle . Basic form In its basic and easiest to remember form, Brahmagupta s formula gives the area K of a cyclic quadrilateral whose sides have lengths a , b , c , d as math K sqrt s a s b s c s d math where s , the semiperimeter , is math s frac a b c d 2 cdot math math s a frac ... may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle all triangles are cyclic , and Brahmagupta s formula converges into Heron s formula. The assertion that the area of the quadrilateral ... to the sides, although if the quadrilateral does not contain the center, the altitude to the longest ... quadrilateral Area of math triangle ADB math Area of math triangle BDC math math frac 1 2 pq sin A frac 1 2 rs sin C. math But since math ABCD math is a cyclic quadrilateral, math angle DAB ... angles of the quadrilateral math K sqrt s a s b s c s d abcd cos 2 theta math where is half ... &minus cos sup 2 sup . It follows from this fact that the area of a cyclic quadrilateral is the maximum possible area for any quadrilateral with the given side lengths. This more general formula is sometimes known as Bretschneider s formula . It is a property of cyclic quadrilateral s and ultimately of inscribed angle s that opposite angles of a quadrilateral sum to 180 . Consequently, in the case of an inscribed quadrilateral, 90 , whence the term math abcd cos 2 theta abcd ... quadrilateral. It is ref J. L. Coolidge, A Historically Interesting Formula for the Area of a Quadrilateral ... 1 over4 ac bd pq ac bd pq , math where p and q are the lengths of the diagonals of the quadrilateral. In a cyclic quadrilateral , math pq ac bd math according to Ptolemy s theorem , and the formula ... more details
File Tetragon measures.svg thumb 230px A quadrilateral. In geometry , Bretschneider s formula is the following expression for the area of a general convex quadrilateral math K sqrt s a s b s c s d abcd cdot cos 2 left frac alpha gamma 2 right . math Here, a , b , c , d are the sides of the quadrilateral, s is the semiperimeter , and math alpha , math and math gamma , math are two opposite angles. Bretschneider s formula works on any convex quadrilateral, whether it is cyclic quadrilateral cyclic or not. The German mathematician Carl Anton Bretschneider discovered the formula in 1842. The formula was also derived in the same year by the German mathematician Karl Georg Christian von Staudt . Proof of Bretschneider s formula Denote the area of the quadrilateral by K . Then we have math begin align K & text area of triangle ADB text area of triangle BDC & frac a d sin alpha 2 frac b c sin gamma 2 . end align math Therefore math 4K 2 ad 2 sin 2 alpha bc 2 sin 2 gamma 2abcd sin alpha sin gamma. , math The Law of Cosines implies that math a 2 d 2 2ad cos alpha b 2 c 2 2bc cos gamma, , math because both sides equal the square of the length of the diagonal BD . This can be rewritten as math frac a 2 d 2 b 2 c 2 2 4 ad 2 cos 2 alpha bc 2 cos 2 gamma 2 abcd cos alpha cos gamma. , math Substituting this in the above formula for math 4K 2 math yields math 4K 2 frac b 2 c 2 a 2 d 2 2 4 ad 2 bc 2 2abcd cdot cos alpha gamma . , math This can be written as math 16K 2 a b c d a b d c a c d b b c d a 16abcd cdot cos 2 left frac alpha gamma 2 right . math Introducing the semiperimeter math s frac a b c d 2 , math the above becomes math 16K 2 16 s a s b s c s d 16abcd cdot cos 2 left frac alpha gamma 2 right math and Bretschneider s formula follows. Related formulas Bretschneider s formula generalizes Brahmagupta s formula for the area of a cyclic quadrilateral , which in turn generalizes Heron s formula for the area of a triangle . External links MathWorld urlname BretschneidersFormula ... more details
Deltoid delta letter delta shaped can refer to The deltoid muscle , a muscle in the shoulder Kite geometry , also known as a deltoid, a type of quadrilateral A deltoid curve , a three sided hypocycloid A leaf shape The deltoid tuberosity , a part of the humerus See also Delta disambiguation John McPhee wrote a book titled The Deltoid Pumpkin Seed 1973 ISBN 0 374 51635 9. disambig it Deltoide ... more details
unref date February 2012 The Q4 element , also known as the bilinear quadrilateral element , is a type of element used in finite element analysis which is used to approximate in a 2D domain the exact solution to a given differential equation . The element consists of a combination of two sets of Lagrange polynomial s, each one used to define the variation of a field in each orthogonal direction of the local referential. category FEM elements Mathanalysis stub ... more details
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