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Cusp





Encyclopedia results for Cusp

  1. Cusp

    Wiktionarypar cusp Cusp may refer to Beach cusps , a pointed and regular arc pattern of the shoreline at the beach Behavioral cusp psychology an important behavior change with far reaching consequences Catastrophe theory Cusp catastrophe Cusp catastrophe Cusp astrology , a boundary between zodiac signs and houses Cusp dentistry , a pointed structure on a cuspid, premolar, or molar Cusp singularity , geometry and astrophysics a singular point of a curve Cusp form in modular form theory Cusp novel , a science fiction story by Robert A. Metzger Cusps of heart valves , leaflets of a heart valve Cuspidal representation , a generalization of cusp forms in the theory of automorphic representations CUSP Project , Carleton University Simulator Project disambig fr Cusp it Cuspide ...   more details



  1. Cusp of Carabelli

    Image Carabelli.jpg thumb Diagram indicating cusp of Carabelli The cusp of Carabelli , or Carabelli s tubercle , or tuberculus anomalus of Georg Carabelli is a small additional cusp dentistry cusp at the Commonly used terms of relationship and comparison in dentistry mesiopalatal line angle of maxillary first molar s. This extra cusp is usually found on the first molar, and becomes progressively less likely in the second, third molars. This cusp is entirely absent in some individuals and present in others in a variety of forms. In some cases, Carabelli s cusp may rival the main cusps in size. Other related forms include ridges, pits, or furrows. This additional cusp was first described in 1842 by the Hungarian Georg Carabelli Carabelli Gy rgy , the court dentist of the Austrian Empire Austrian Emperor Franz. The cusp of Carabelli is a heritable feature. Kraus 1951 proposed that Zygosity homozygosity of a gene is responsible for a pronounced tubercle, whereas the Zygosity heterozygote shows slight grooves, pits, tubercles or bulge. Later studies showed that the development of this trait is affected by multiple genes. Carabelli s cusp is most common among Europeans 75 85 of individuals and rarest in Pacific Islands 35 45 . This cusp may also be found in dogs and cats. Further reading Simon Hillson. 1996. Dental Anthropology . Cambridge University Press. Tooth anatomy Category Teeth ja pt Tub rculo de Carabelli ...   more details



  1. Cusp (dentistry)

    Image Cusp tips.JPG 250px thumb right The teeth of the right side of the mouth, shown contacting the teeth in the opposing jaw with their cusp tips. A cusp is an Commonly used terms of relationship and comparison in dentistry occlusal or Commonly used terms of relationship and comparison in dentistry incisal eminence on a tooth. canine tooth Canine teeth, otherwise known as cuspids , each possess a single cusp, while premolar s, otherwise known as bicuspids , possess two each. Molars normally possess either four or five cusps. In certain populations the maxilla ry molars, especially first molar s, will possess a fifth cusp situated on the Commonly used terms of relationship and comparison in dentistry mesiolingual cusp known as the Cusp of Carabelli . References Ash, Major M. Nelson, Stanley. WHEELER S DENTAL ANATOMY, PHYSIOLOGY AND OCCLUSION, 8th edition. Category Teeth dentistry stub Tooth anatomy ko pt C spide tr T berk l ...   more details



  1. Cusp (astrology)

    Unreferenced date December 2007 In astrology , a cusp from the Latin for spear or point is the imaginary line that separates a pair of consecutive Astrological sign sign s in the zodiac or House astrology house s in the horoscope . Because the solar disc has a diameter of approximately half a degree, it is possible for the Sun to straddle the cusp as it moves across the sky. When this occurs at the moment of birth such a person is said to be born on the cusp and some believe that their life is influenced by the characteristics of both signs. For example, if an individual was born when the Sun by convention the point at the centre of the Solar disc was located at 29 degrees, 50 minutes Gemini astrology Gemini , then one might say that he was born on the cusp of Gemini and Cancer astrology Cancer . Much of the Solar disc was actually in Cancer even though the centre was in Gemini. Although the term cusp is universally used for the boundaries of signs, not all astrologers agree that an object can ever be included in more than one sign. Many consider relevant only the location of the Sun s centre, which must be entirely in one sign, and would describe the natal Sun in the example as simply being in Gemini. If late degrees of Gemini have a Cancer like character, they would describe that as simply the nature of that part of Gemini rather than some influence spilling over from the next sign. On the other hand, astrologers who consider objects on the cusp to be meaningfully different ... the boundary. That point of view may consider the Sun to be on the cusp even when its centre is as much ... a degree in diameter on the cusp despite no part of the object being in the adjacent sign. Their claim is that the influence of the cusp gets weaker but does not suddenly disappear as the object gets further from the cusp. A similar debate applies to cusps between houses. The majority of astrologers ... who treat Sun positions near the cusp as distinct. Sources http www.astrologyzine.com astrology ...   more details



  1. Cusp Conference

    Cusp Conference is an annual gathering of thinkers, innovators, creators, skeptics, believers, visionaries and explorers from the arts, sciences, technology, business and design. A conference about the design of everything ref name GapersBlock cite web url http gapersblock.com ac 2008 09 17 review cusp conference 2008 title Cusp Conference 2008 The Design of Everything publisher Gapers Block date 17 September 2008 accessdate 2011 02 17 ref created and hosted by design firm smbolic ref name MetropolisMag cite web url http www.metropolismag.com pov tag cusp title It s a Swamp Thing publisher Metropolis Magazine date 2010 09 29 accessdate 2011 02 17 ref formerly SamataMason ref name DesignEdgeCanada cite web author Val Maloney url http www.designedgecanada.com news 2010 20100823843.shtml title ... herman miller sponsors cusp conference in chicago title Herman Miller Sponsors CUSP Conference in Chicago publisher Herman Miller date 2010 09 27 accessdate 2011 02 17 ref Cusp is centered around the idea ... force. Cusp Conference presenters have touched on topics as diverse as landscape waste, contemporary ... cite web url http pitchdesignunion.com ?p 4170 title Cusp Conference 2010 Recap publisher Pitch Design ... AllBeef cite web author Jacquie Wallace url http allbeefmedia.com the blog riding the cusp highlights from chicagos coolest design conf.html title Riding the Cusp Highlights from Chicago s Coolest Design ... url http evilmonito.com 2010 09 26 cusp conference dont waste your thing title CUSP Conference ... and taste and serious games. History Launched in 2008, Cusp Conference presenters and performers ... url http ijustine.com cusp conference title Cusp Conference publisher iJustine date 2008 09 12 accessdate ... article 100432 Cusp Conference title Cusp Conference publisher Design Taxi date 2008 09 11 accessdate ... AIGA cite web url http www.aigachicago.org node 1902 title Cusp Conference 2008 publisher AIGA Chicago ... official website http designchat.info dc 69 cusp conference 2010 Cusp Conference on DesignChat ...   more details



  1. Cusp form

    In number theory , a branch of mathematics , a cusp form is a particular kind of modular form , distinguished in the case of modular forms for the modular group by the vanishing in the Fourier series expansion see q expansion q expansion math Sigma a n q n math of the constant coefficient a sub 0 sub . This Fourier expansion exists as a consequence of the presence in the modular group s action on the upper half plane of the transformation math z mapsto z 1. math For other groups, there may be some translation through several units, in which case the Fourier expansion is in terms of a different parameter. In all cases, though, the limit as q &rarr 0 is the limit in the upper half plane as the imaginary part of z &rarr &infin . Taking the quotient by the modular group, say, this limit corresponds to a cusp of a modular curve in the sense of a point added for compactification mathematics compactification . So, the definition amounts to saying that a cusp form is a modular form that vanishes at a cusp. In the case of other groups, there may be several cusps, and the definition becomes a modular form vanishing at all cusps. This may involve several expansions. The dimensions of spaces of cusp forms are in principle computable, via the Riemann Roch theorem . For example, the famous Ramanujan function &tau n arises as the sequence of Fourier coefficients of the cusp form of weight 12 for the modular group, with a sub 1 sub 1. The space of such forms has dimension 1, which means this definition is possible and that accounts for the action of Hecke operator s on the space being by scalar multiplication Mordell s proof of Ramanujan s identities . Explicitly it is the modular discriminant &Delta z , q , which represents up to a normalizing constant the discriminant of the cubic on the right side of the Weierstrass equation of an elliptic curve and the 24 th power of the Dedekind ... function , with the normalization &tau 1 1. In the larger picture of automorphic form s, the cusp ...   more details



  1. Cusp neighborhood

    Context date October 2008 Unreferenced date October 2008 In mathematics , a cusp neighborhood is defined as a set of points near a cusp singularity cusp . Cusp neighborhood for a Riemann surface The cusp neighborhood for a hyperbolic Riemann surface can be defined in terms of its Fuchsian model . Suppose that the Fuchsian group G contains a parabolic element g. For example, the element math t in SL 2, mathbb Z math where math t z begin pmatrix 1 & 1 0 & 1 end pmatrix z frac 1 cdot z 1 0 cdot z 1 z 1 math is a parabolic element. Note that all parabolic elements of math SL 2, mathbb C math are conjugacy class conjugate to this element. That is, if math g in SL 2, mathbb C math is parabolic, then math g h 1 th math for some math h in SL 2, mathbb C math . The set math U z in mathbb H Im z 1 math where math mathbb H math is the upper half plane has math gamma U cap U emptyset math for any math gamma in G langle g rangle math where math langle g rangle math is understood to mean the group mathematics group generated by g . That is, acts properly discontinuously on U . Because of this, it can be seen that the projection of U onto H G is thus math E U langle g rangle math . Here, E is called the neighborhood of the cusp corresponding to g . Note that the hyperbolic area of E is exactly 1, when computed using the canonical Poincar metric . This is most easily seen by example consider the intersection of U defined above with the fundamental domain math left z in H left z right 1, , left , mbox Re z , right frac 1 2 right math of the modular group , as would be appropriate for the choice of T as the parabolic element. When integrated over the volume element math d mu frac dxdy y 2 math the result is trivially 1. Areas of all cusp neighborhoods are equal to this, by the invariance of the area under conjugation. Category Hyperbolic geometry Category Riemann surfaces ...   more details



  1. Cusp (novel)

    orphan date August 2010 Cusp is a science fiction novel written by Robert A. Metzger , in the category of hard science fiction. It deals with two perpendicular rings running along the Earth s surface, that act as cosmic jets, using ionized hydrogen . In this universe, the fusion of organic and non organic material is an everyday thing. Multiple characters are portrayed in the story, and it is told from Third person narrative 3rd person . Literary significance and reception Carl Hays reviewing for Booklist said that Metzger s background as a telecommunications scientist enables a brilliant, sprawling vision of humanity in the late twenty first century. ref name Hays cite journal title CUSP Book last Hays first Carl date January 1, 2005 journal Booklist volume 101 issue 9 10 pages 834 issn 00067385 ref Kirkus Reviews was mixed in their coverage saying that Cusp was Overcomplicated by several orders of magnitude, with anonymous characters mystifyingly associated with a ferocious and largely unfathomable plot. Still, minds will boggle at the extravagance of Metzger s imagination. ref name Kirkus Reviews cite journal date November 15, 2004 title CUSP Book journal Kirkus Reviews volume 72 issue 22 pages 1072 issn 00426598 ref Notes reflist DEFAULTSORT Cusp Novel Category 2005 novels Category 2000s science fiction novels Category 21st century American novels 2000s sf novel stub ...   more details



  1. Talon cusp

    Infobox Disease Name PAGENAME Image Caption DiseasesDB ICD10 ICD10 K 00 2 k 00 ICD9 ICD9 520.2 ICDO OMIM MedlinePlus eMedicineSubj eMedicineTopic MeshID A talon cusp , also known as an eagle s talon , is an extra cusp on an anterior tooth . The term refers to the same condition as dens evaginatus , but the talon cusp is the manifestation of dens evaginatus on anterior teeth. The incidence has been found to range from less than 1 to 6 of the population. ref name neville78 Neville, B.W., D. Damm, C. Allen, J. Bouquot. Oral & Maxillofacial Pathology . Second edition. 2002. Page 78. ISBN 0 7216 9003 3. ref Of all cases, 55 occur on the permanent maxillary lateral incisor , and 33 occur on the permanent maxillary central incisor . They are found rarely in primary teeth . References div class references small references div Dentistry stub Tooth disease Category Oral pathology zh min nan Eng ji u h ng k th u ...   more details



  1. Cusp (singularity)

    Image cusp.svg thumb right 200px An ordinary cusp on the curve x sup 3 sup y sup 2 sup 0 In the singularity theory mathematical theory of singularities a cusp is a type of singular point of a curve . Cusps are local singularities in that they are not formed by self intersection points of the curve. The plane curve cusps are all diffeomorphic to one of the following forms x sup 2 sup   &minus   y sup 2 k 1 sup   0, where k   1 is an integer . More general background Consider a smooth function smooth real valued function of two variable s, say f x ,  y where x and y are real number s. So f is a function from the plane to the line. The space of all such smooth functions is group action acted upon by the group mathematics group of diffeomorphism s of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the Domain of a function source ...   1 is an integer. Examples Image Caustic00.jpg thumb right 200px An ordinary cusp occurring as the Caustic optics caustic of light rays in the bottom of a teacup. An ordinary cusp is given by x ... cusp points. By generic we mean that an Open set open and Dense set dense set of all caustics comprise smooth points and ordinary cusp points. Caustics are, informally, points of exception brightness ... cusp is also important in wavefront s. A wavefront can be shown to generically comprise smooth points and ordinary cusp points. By generic we mean that an open set open and Dense set dense set of all wavefronts comprise smooth points and ordinary cusp points. A rhamphoid cusp coming from the Greek ... 4 sub singularity. These cusps are non generic as caustics and wavefronts. The rhamphoid cusp and the ordinary cusp are non diffeomorphic. For a type A sub 4 sub singularity we need f to have a degenerate ... level set will be a rhamphoid cusp. See also Catastrophe theory Cusp catastrophe Cusp catastrophe ... DEFAULTSORT Cusp Singularity Category Algebraic curves Category Singularity theory bg ...   more details



  1. Behavioral cusp

    A behavioral cusp is any behavior change that brings an organism s behavior into contact with new contingencies that have far reaching consequences. ref name rosales97 A behavioral cusp is a special type of behavior change because it provides the learner with opportunities to access 1 new reinforcers, 2 new contingencies 3 new environments, 4 new related behaviors generativeness ref Alessi, G. 1987 ... and change due to the simple passage of time, such as developmental milestones . The cusp is a behavior ... Cusps. The Behavior Analyst Today , 5 3 , 244 253 http www.baojournal.com BAO ref The idea of the cusp ... development A behavioral cusp as conceptualized by Jesus Rosales Ruiz & Donald Baer in 1997 is an important ... cusp, like the reinforcer , is apprehended by its effects. Whereas a reinforcer acts on a single response or a group of related responses, the effects of a behavioral cusp regulate a large number ... or cusp , Pel accessed 1 new environments, 2 new reinforcers, 3 new soccer moves, 4 dropped competing ... cusp The following properties are special features of a behavioral change that lead to more change ... responses, functions, values or response products derived from the original cusp response. For a behavior .... Competition with archaic behaviors Behavior competition is the ability of cusp behaviors killer ... in values and behaviors of the stakeholder resulting from a cusp in the learner. The initial and gradually ... preexisting behavioral repertoires obsolete. A behavioral cusp is an important behavior change ... be learned. Applications Life span development guidelines The behavioral cusp has implications ... with the chronology of behaviors, the concept of behavioral cusp is concerned with the fitness of the behavior ... child s cusp may be another child s waste of time. Thus, there is a great need for empirically based ..., will reveal a strong dependence on the initial conditions selected by a cusp specialist butterfly effect . class wikitable Cusp Applications Education Teacher Training Post Curriculum instructional ...   more details



  1. File:Cusp in teacup.gif

    Summary Image of a cusp created by reflection of light a caustic optics caustic in the bottom of a tea cup. Author User Salix alba . Licensing GFDL self with disclaimers migration relicense ...   more details



  1. Terry Riley: The Cusp of Magic

    Infobox Album See Wikipedia WikiProject Albums Name Terry Riley The Cusp of Magic Type studio Artist Kronos Quartet Cover kronos cusp.jpg Released start date 4 February 2008 Recorded Genre Contemporary classical Length Label Nonesuch Records Nonesuch small 360508 small Producer Judith Sherman Reviews Last album Kronos Quartet Plays Sigur R s br 2007 This album Terry Riley The Cusp of Magic br 2008 Next album Floodplain album Floodplain br 2009 Terry Riley The Cusp of Magic is a studio album by the Kronos Quartet , an album length recording of a collaboration between the quartet and American composer Terry Riley . Terry Riley and the Kronos Quartet Terry Riley and the Kronos Quartet have been collaborating since 1978, when Riley taught Musical composition composition , Musical improvisation improvisation , and Hindustani classical music at Mills College in Oakland, California , and the quartet were artists in residence. Both parties benefitted from the exhange. In the words of Joan Jeanrenaud Kronos cellist until 1998 , Terry shaped how Kronos shaped the music we played the Kronos Quartet, in turn, helped Riley to move beyond the Minimalist music minimalism of his early period, ref name gillmore cite album notes title Terry Riley Requiem for Adam albumlink bandname Kronos Quartet year 2001 notestitle url first Bob last Gillmore authorlink coauthors pages format publisher Nonesuch Records Nonesuch publisherid location mbid ref an observation made also by K. Robert Schwarz in a long piece in the New York Times on the occasion of an overview of the composer s career By 1984, when he completed Cadenza on the Night Plain, he had turned his back on the Minimalism of In C, instead exploring sonic realms stretching from the long breathed lyricism of North India to the spiky, fragmented development of Bartok. ref name schwarz cite news last K. Robert first Schwarz coauthors title ... credits music credits Terry Riley title1 I. The Cusp of Magic note1 length1 10 02 title2 II. Buddha ...   more details



  1. Cusps of heart valves

    Infobox Anatomy Name Cusps of heart valves Latin GraySubject GrayPage Image Gray495.png Caption Base of ventricles exposed by removal of the atria. Valves visible on top of heart. Image2 Gray497.png Caption2 Aorta laid open to show the semilunar valves. Note that captions don t align with current terminology. System Precursor MeshName MeshNumber DorlandsPre DorlandsSuf The cusps of the heart valves serve to seal the heart valve s when closed. There are three cusps for each valve except for the mitral valve , which has only two hence its alternate name, bicuspid valve . Nodules are located at the tip of the valve, to form a tighter seal. Semilunar valves pulmonary valve ref SUNYAnatomyLabs 20 21 01 02 Heart The Pulmonic Valve ref right cusp left cusp anterior cusp aortic valve ref SUNYAnatomyLabs 20 29 01 04 Heart The Aortic Valve and Aortic Sinuses ref . Note that one is absent in the condition bicuspid aortic valve . right cusp left cusp posterior cusp or noncoronary cusp Atrioventricular valves tricuspid valve right av anterior cusp or infundibular cusp posterior cusp or marginal cusp septal cusp or medial cusp mitral valve left av anterior cusp posterior cusp Additional images gallery Image Heart short axis aorta.svg Heart short axis aorta Image Heart valves.png Cusps of heart valves gallery References references External links SUNYAnatomyFigs 20 07 00 Valves of the heart. Heart Category Cardiac anatomy Category Valves circulatory stub ...   more details



  1. Gnarled enamel

    Gnarled enamel is a description of tooth enamel enamel seen in histology histologic sections of a tooth underneath a cusp dentistry cusp . The appearance of enamel appears different and very complex under the cusp, but this is not due to a different arrangement of dental tissues. Instead, the enamel still has the same arrangement of enamel rod s. The strange appearance results from the lines of enamel rods directed vertically under a cusp and from their orientation in a small circumference. References Cate, A.R. Ten. Oral Histology development, structure, and function. 5th ed. 1998. ISBN 0 8151 2952 1. Category Dentistry subjects Category Histology Category Mouth dentistry stub ...   more details



  1. File:Class II.jpg

    Summary Dr. Vipin C. P. class II human Molar relationsship. the mesiobuccal cusp of upper molar rest mesial to the lower molars Licensing PD self date December 2006 ...   more details



  1. Metacone

    Unreferenced date March 2007 image Tooth Picturewlabels.jpg thumb 500px left Right upper molar showing the four main upper molars cusps. The metacone is a cusp dentistry cusp on the molars of the upper dentition in hominids . It is found at the buccal distal area of the tooth. The crests between the cusps are adaptations for slicing food during occlusion or mastication chewing . Other cusps of the upper dentition of hominids include the paracone , hypocone , and the protocone . Category Teeth dentistry stub ...   more details



  1. File:Kronos cusp.jpg

    Summary album cover fur REQUIRED Article Terry Riley The Cusp of Magic Use Infobox HIGHLY RECOMMENDED Source http www.nonesuch.com albums terry riley the cusp of magic ADDITIONAL INFORMATION Name Artist Kronos Quartet Label Nonesuch Graphic Artist Frank Olinsky Item front cover Type CD Website Owner Commentary OVERRIDE FIELDS Description Portion Low resolution Purpose Replaceability other information Licensing Non free album cover ...   more details



  1. Mandibular second premolar

    three cusps but can have two as well. The three cusp variety has one large cusp on the buccal with two smaller lingual cusps. The mesiolingual cusp is twice the size of the disolingual cusp. Viewed from ..., particularly on the lingual. The occlusal table the area bounded by the cusps, cusp ridges, and marginal ... from the buccal the buccal cusp tip is centered mesiodistally. The buccal cusp ridges exhibit ... is in the middle third of the tooth not the middle third of the lingual cusp . When divided into thirds from the buccal height of contour to the lingual height of contour, the buccal cusp is at the contact ... and lingual thirds. The two cusp variety generally has a groove pattern shaped like a U or H . Viewed from the occlusal it is more rounded in general and its lingual cusp is positioned slightly to the mesial, while the occlusal table remains squared. Viewed from the buccal the buccal cusp is centered over the root as in the three cusp variety. Viewed from the mesial or distal its heights of contour are similar to the three cusp variety. Sometimes, premolars are referred to as bicuspids . Even though ...   more details



  1. Lewis offset

    Multiple issues expert January 2011 lead rewrite January 2011 The Lewis offset is a term for the portion of the central groove on a permanent mandibular first molar which lies between the two central pits. It lies at an angle to the mesio distal axis of the tooth, and causes the mesial portion of the central groove to be located further buccally than the distal portion. This bucco lingual shift correlates with a relative difference in size between the mesial and distal cusps on these teeth the mesiolingual cusp is larger than the mesiobuccal cusp, but the distobuccal cusp is larger than the distolingual cusp. It also allows for the buccal groove to be located mesial to the lingual groove which is mandatory to accommodate the relative sizes of the three cusps on the buccal and two cusps on the lingual of the occlusal surface of the tooth. The offset is named for Dr. Christopher S. Lewis, a Mercer Island, WA dentist and longtime faculty member in Dental Anatomy at the University of Washington School of Dentistry . File DrawingofMand1stMolar.jpg References reflist Ash, Major M. and Stanley J. Nelson, 2003. Wheeler s Dental Anatomy, Physiology, and Occlusion. 8th edition. Tooth anatomy DEFAULTSORT Lewis Offset Category Teeth dentistry stub nl Eerste molaar pt Primeiro molar inferior ...   more details



  1. Hypocone

    Unreferenced date December 2007 Image Tooth Picturewlabels.jpg thumb 250px Right upper molar showing the four main upper molars cusps The hypocone is the name for a main cusp dentistry cusp found on the Molar tooth molars of the upper dentition of hominids . It is found on the distal lingual side of the tooth. It fits into the grooves of the lower dentition and is an adaptation for the overall grinding and tearing of foods using the Occlusion dentistry occlusal chewing side of the tooth surface during occlusion or mastication chewing . Its strength is due to the thickness of the Tooth enamel enamel which differs among species of hominids. dentistry stub Category Teeth ...   more details



  1. Protocone

    image Tooth Picturewlabels.jpg thumb 500px right Right upper molar showing the four main upper molars cusps. The protocone is a cusp dentistry cusp of the molars of the upper dentition in Placental and Marsupial vertebrates ref Gavin Prideaux, Systematics and Evolution of the Sthenurine Kangaroos April 1, 2004 . UC Publications in Geological Sciences. Paper vol 146. http repositories.cdlib.org ucpress ucpgs vol 146 p.16 ref .It is found at the mesiolingual area of the tooth. The crests between the cusps are adaptations for slicing food during occlusion dentistry occlusion or mastication chewing . Other cusps of the upper dentition of hominids include the paracone , hypocone , and the metacone . References references Category Teeth dentistry stub ...   more details



  1. Vertex (curve)

    Other uses Vertex disambiguation Image Ellipse evolute.svg right thumb 240px An ellipse red and its evolute blue . The dots are the vertices of the curve, each corresponding to a cusp on the evolute. In the geometry of curve s a vertex is a point of where the first derivative of curvature is zero. This is typically a local Maxima and minima maximum or minimum of curvature. Other special cases may occur, for instance when the second derivative is also zero, or when the curvature is constant. For a circle which has constant curvature, every point is a vertex. The four vertex theorem states that every closed curve must have at least four vertices. Vertices are points where the curve has Contact mathematics Contact between curves 4 point contact with the osculating circle at that point. The evolute of a curve will have a cusp singularity cusp when the curve has a vertex. The symmetry set has endpoints at the cusps corresponding to the vertices, and the medial axis , a subset of the symmetry set also has its endpoints in the cusps. If a curve is reflection symmetry bilaterally symmetric , it will have a vertex at the point or points where the axis of symmetry crosses the curve. Thus, the notion of a vertex for a curve is closely related to that of an vertex optics optical vertex , the point where an optical axis crosses a Lens optics lens surface. References unreferenced date November 2007 geometry stub Category Curves de Scheitelpunkt sl Teme ...   more details



  1. Chinese University Student Press

    POV date December 2007 Chinese University Student Press CUSP, is a magazine published by the Chinese University of Hong Kong Students Union. The CUSP is considered one of the most liberal magazine published in Hong Kong, and sparked controversies because of its publication of the Sex Column. References http www.foxnews.com story 0,2933,272955,00.html Hong Kong Authorities Ponder Labeling Bible Indecent , Fox News http www.stuff.co.nz 4062957a4560.html Bible drawn into Hong Kong sex publication row , Reuters http www.wdcmedia.com pressReleaseArticle.php?ID 353 Bible Nazis Seek Worldwide Ban On The Bible , WDC Media News External links http www.cusp.hk CUSP Official Website http www.truthbible.net Bible complain website http euler.truthbible.net The blog of volunteer organizer at 71 demonstration, still active http groups.google.com group NGLITHK NGLITHK Google group Category The Chinese University of Hong Kong Category Hong Kong magazines Category Liberalism Category Publications with year of establishment missing zh ...   more details



  1. Angular house

    The seventh house, of which the cusp is often but not always the Descendant astrology Descendant , shows .... ref Tenth house The tenth house, of which is often but not always the cusp is also the Midheaven ...   more details




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