Right Interior Exterior
Adjacent Vertical Complementary Supplementary
Dihedral
A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes. The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called "wings") are upwardly inclined to the lateral axis; when downwardly inclined they are said to be at a negative dihedral angle.
When the two intersecting planes are described in terms of Cartesian coordinates by the two equations
the dihedral angle, φ φ --> {\displaystyle \varphi } between them is given by:
and satisfies 0 ≤ ≤ --> φ φ --> ≤ ≤ --> π π --> / 2. {\displaystyle 0\leq \varphi \leq \pi /2.} It can easily be observed that the angle is independent of d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} .
Alternatively, if nA and nB are normal vector to the planes, one has
where nA · nB is the dot product of the vectors and |nA| |nB| is the product of their lengths.[1]
The absolute value is required in above formulas, as the planes are not changed when changing all coefficient signs in one equation, or replacing one normal vector by its opposite.
However the absolute values can be and should be avoided when considering the dihedral angle of two half planes whose boundaries are the same line. In this case, the half planes can be described by a point P of their intersection, and three vectors b0, b1 and b2 such that P + b0, P + b1 and P + b2 belong respectively to the intersection line, the first half plane, and the second half plane. The dihedral angle of these two half planes is defined by
and satisfies 0 ≤ ≤ --> φ φ --> < π π --> . {\displaystyle 0\leq \varphi <\pi .} In this case, switching the two half-planes gives the same result, and so does replacing b 0 {\displaystyle \mathbf {b} _{0}} with − − --> b 0 . {\displaystyle -\mathbf {b} _{0}.} In chemistry (see below), we define a dihedral angle such that replacing b 0 {\displaystyle \mathbf {b} _{0}} with − − --> b 0 {\displaystyle -\mathbf {b} _{0}} changes the sign of the angle, which can be between −π and π.
In some scientific areas such as polymer physics, one may consider a chain of points and links between consecutive points. If the points are sequentially numbered and located at positions r1, r2, r3, etc. then bond vectors are defined by u1=r2−r1, u2=r3−r2, and ui=ri+1−ri, more generally.[2] This is the case for kinematic chains or amino acids in a protein structure. In these cases, one is often interested in the half-planes defined by three consecutive points, and the dihedral angle between two consecutive such half-planes. If u1, u2 and u3 are three consecutive bond vectors, the intersection of the half-planes is oriented, which allows defining a dihedral angle that belongs to the interval (−π, π]. This dihedral angle is defined by[3]
or, using the function atan2,
This dihedral angle does not depend on the orientation of the chain (order in which the point are considered) — reversing this ordering consists of replacing each vector by its opposite vector, and exchanging the indices 1 and 3. Both operations do not change the cosine, but change the sign of the sine. Thus, together, they do not change the angle.
A simpler formula for the same dihedral angle is the following (the proof is given below)
or equivalently,
This can be deduced from previous formulas by using the vector quadruple product formula, and the fact that a scalar triple product is zero if it contains twice the same vector:
Given the definition of the cross product, this means that φ φ --> {\displaystyle \varphi } is the angle in the clockwise direction of the fourth atom compared to the first atom, while looking down the axis from the second atom to the third. Special cases (one may say the usual cases) are φ φ --> = π π --> {\displaystyle \varphi =\pi } , φ φ --> = + π π --> / 3 {\displaystyle \varphi =+\pi /3} and φ φ --> = − − --> π π --> / 3 {\displaystyle \varphi =-\pi /3} , which are called the trans, gauche+, and gauche− conformations.
In stereochemistry, a torsion angle is defined as a particular example of a dihedral angle, describing the geometric relation of two parts of a molecule joined by a chemical bond.[4][5] Every set of three non-colinear atoms of a molecule defines a half-plane. As explained above, when two such half-planes intersect (i.e., a set of four consecutively-bonded atoms), the angle between them is a dihedral angle. Dihedral angles are used to specify the molecular conformation.[6] Stereochemical arrangements corresponding to angles between 0° and ±90° are called syn (s), those corresponding to angles between ±90° and 180° anti (a). Similarly, arrangements corresponding to angles between 30° and 150° or between −30° and −150° are called clinal (c) and those between 0° and ±30° or ±150° and 180° are called periplanar (p).
The two types of terms can be combined so as to define four ranges of angle; 0° to ±30° synperiplanar (sp); 30° to 90° and −30° to −90° synclinal (sc); 90° to 150° and −90° to −150° anticlinal (ac); ±150° to 180° antiperiplanar (ap). The synperiplanar conformation is also known as the syn- or cis-conformation; antiperiplanar as anti or trans; and synclinal as gauche or skew.
For example, with n-butane two planes can be specified in terms of the two central carbon atoms and either of the methyl carbon atoms. The syn-conformation shown above, with a dihedral angle of 60° is less stable than the anti-conformation with a dihedral angle of 180°.
For macromolecular usage the symbols T, C, G+, G−, A+ and A− are recommended (ap, sp, +sc, −sc, +ac and −ac respectively).
A Ramachandran plot (also known as a Ramachandran diagram or a [φ,ψ] plot), originally developed in 1963 by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan,[7] is a way to visualize energetically allowed regions for backbone dihedral angles ψ against φ of amino acid residues in protein structure. In a protein chain three dihedral angles are defined:
The figure at right illustrates the location of each of these angles (but it does not show correctly the way they are defined).[8]
The planarity of the peptide bond usually restricts ω to be 180° (the typical trans case) or 0° (the rare cis case). The distance between the Cα atoms in the trans and cis isomers is approximately 3.8 and 2.9 Å, respectively. The vast majority of the peptide bonds in proteins are trans, though the peptide bond to the nitrogen of proline has an increased prevalence of cis compared to other amino-acid pairs.[9]
The side chain dihedral angles are designated with χn (chi-n).[10] They tend to cluster near 180°, 60°, and −60°, which are called the trans, gauche−, and gauche+ conformations. The stability of certain sidechain dihedral angles is affected by the values φ and ψ.[11] For instance, there are direct steric interactions between the Cγ of the side chain in the gauche+ rotamer and the backbone nitrogen of the next residue when ψ is near -60°.[12] This is evident from statistical distributions in backbone-dependent rotamer libraries.
Every polyhedron has a dihedral angle at every edge describing the relationship of the two faces that share that edge. This dihedral angle, also called the face angle, is measured as the internal angle with respect to the polyhedron. An angle of 0° means the face normal vectors are antiparallel and the faces overlap each other, which implies that it is part of a degenerate polyhedron. An angle of 180° means the faces are parallel, as in a tiling. An angle greater than 180° exists on concave portions of a polyhedron.
Every dihedral angle in an edge-transitive polyhedron has the same value. This includes the 5 Platonic solids, the 13 Catalan solids, the 4 Kepler–Poinsot polyhedra, the two quasiregular solids, and two quasiregular dual solids.
Given 3 faces of a polyhedron which meet at a common vertex P and have edges AP, BP and CP, the cosine of the dihedral angle between the faces containing APC and BPC is:[13]
This can be deduced from the spherical law of cosines.
El logo del Proyecto Fedora. Proyecto Fedora es la comunidad responsable de la producción de la distribución Fedora, junto con una variedad de otros proyectos. El Proyecto Fedora es el resultado de la fusión entre Red Hat Linux y el antiguo Proyecto Fedora Linux en septiembre de 2003, y es patrocinado oficialmente por Red Hat, quien tiene un grupo de empleados trabajando en el código del proyecto. El Proyecto Fedora Linux desarrollaba paquetes extra para viejas distribuciones de Red Hat Linu…
رأب الفقرة عن طريق الجلد Percutaneous vertebroplasty نموذج اعداد جناح التدخل لجراحة رأب الحدبة تعديل مصدري - تعديل رأبُ الفقرة عن طريق الجلد رأبُ الفقرة ورأبُ الحدبة هما إجراءان مشابهان لإجراءات العمود الفقري الطبية، التي يتم فيها حقن ملاط العظم في الفقرة المكسورة من خلال تجويف صغير…
Cet article concerne l'état liquide. Pour l'argent liquide (pièces et billets de banque), voir Monnaie fiduciaire. Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Cet article ne cite pas suffisamment ses sources (juin 2016). Si vous disposez d'ouvrages ou d'articles de référence ou si vous connaissez des sites web de qualité traitant du thème abordé ici, merci de compléter l'article en donnant les références utiles à sa vérifiabilité et en les li…
село Четвертаково Четвертаково Країна Росія Суб'єкт Російської Федерації Нижньогородська область Муніципальний район Арзамаський район Поселення Слизневська сільрада Код ЗКАТУ: 22203872009 Код ЗКТМО: 22603472141 Основні дані Населення ▼ 68 Поштовий індекс 607244 Телефонний код +7&…
Pakistani State owned weapons manufacturer Pakistan Ordnance FactoriesOfficial logo of Pakistan Ordnance FactoriesNative nameUrdu: پاکستان آرڈیننس فیکٹریاںTypeState-owned companyIndustryFirearms, Defense, MachineryFounded1951; 72 years ago (1951)HeadquartersWah Cantonment, Punjab, PakistanArea servedworldwideKey peopleLt General Syed Tahir Hameed Shah (Chairman)ProductsPistols, Rifles, Submachine gun, Machine gun, Shotguns, Munitions, Explosives, Machine t…
Фінал Кубка УЄФА 2000Турнір Кубок УЄФА 1999—2000 «Галатасарай» «Арсенал» 0 0 Серія пенальті«Галатасарай» 4 - 1 «Арсенал»Дата 17 травня 2000Стадіон «Паркен», (Копенгаген)Арбітр Антоніо Лопез НьєтоГлядачі 38,919← 1999 2001 → Фінал Кубка УЄФА 1999—2000 — фінальний матч двадцять дев'ятог…
Hans Bock der Ältere: Bildnis des Thomas Platter, 1581. Kunstmuseum Basel Thomas Platter der Ältere (* 10. Februar 1499 in Grächen/Wallis; † 26. Januar 1582 in Basel) war ein schweizerischer humanistischer Gelehrter und hinterliess eine Autobiographie, in der er seinen exemplarischen Werdegang vom Hirtenkind und fahrenden Schüler zum Anhänger der Reformation, Buchdrucker und Lehrer der alten Sprachen in Basel beschreibt. Inhaltsverzeichnis 1 Leben 2 Lebensbeschreibung 3 Literatur 4 Weblin…
Віллі ван де Керкгоф Віллі ван де Керкгоф Особисті дані Повне ім'я Вільгельмус Антоніус ванде Керкгоф Народження 16 вересня 1951(1951-09-16) (72 роки) Гелмонд, Нідерланди Зріст 182 см Вага 78 кг Громадянство Нідерланди Позиція півзахисник Інформація про клуб Поточний клуб…
Coventry-class Royal Navy frigate For other ships with the same name, see HMS Active. Active (right) engaging the Spanish frigate Hermione (centre) in 1762: sketch by Richard Wright History Great Britain NameHMS Active Ordered6 May 1757 BuilderThomas Stanton, Rotherhithe Laid down13 June 1757 Launched11 January 1758 Completed2 March 1758 at Deptford Dockyard CommissionedJanuary 1758 FateTaken by the French off San Domingo 1 September 1778 France NameActive Acquired1778 by capture FateBroken up 1…
هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (أبريل 2019) إيمي تومسون معلومات شخصية الميلاد 28 أكتوبر 1958 (65 سنة) ميامي مواطنة الولايات المتحدة الحياة العملية المدرسة الأم جامعة إيداهو[1] المهنة روائية
SÉCULOS: Século XV — Século XVI — Século XVII DÉCADAS: 1470 • 1480 • 1490 • 1500 • 1510 • 1520 • 1530 • 1540 • 1550 • 1560 • 1570 ANOS: 1519 • 1520 • 1521 • 1522 • 1523 • 1524 • 1525 • 1526 • 1527 • 1528 • 1529 Outros projetos Wikimedia também contêm material sobre este tema: Textos originais no Wikisource Wikisource 1524 em outros calendários Calendário gregoriano 1524 MDXXIV Ab urbe condita 2277 Calendário arménio 973 ̵…
Elena Bissolati Elena Bissolati (2019) Zur Person Geburtsdatum 10. Januar 1997 Nation Italien Italien Disziplin Bahn / Straße Wichtigste Erfolge Paracycling-Bahnweltmeisterschaften 2023 – Mixed-Sprint Letzte Aktualisierung: 24. Oktober 2023 Elena Bissolati (* 10. Januar 1997 in Cremona) ist eine italienische Radsportlerin, die vorrangig auf der Bahn aktiv ist. Inhaltsverzeichnis 1 Sportlicher Werdegang 2 Erfolge 2.1 Bahn 2.2 Paracycling (Bahn) 3 Teams 4 Weblinks 5 Einzelnachweise Sp…
لأماكن أخرى بنفس الاسم، انظر أسد أباد (توضيح). أسد أباد اسداباد - قرية - تقسيم إداري البلد إيران المحافظة يزد المقاطعة أبركوه الناحية Bahman القسم الريفي قسم اسفندار الريفي إحداثيات 30°56′10″N 53°26′19″E / 30.93611°N 53.43861°E / 30.93611; 53.43861 السكان التعداد السكاني 798…
Artikel ini sebagian besar atau seluruhnya berasal dari satu sumber. Diskusi terkait dapat dibaca pada the halaman pembicaraan. Tolong bantu untuk memperbaiki artikel ini dengan menambahkan rujukan ke sumber lain yang tepercaya. Dalam politik, mandat adalah wewenang yang diberikan oleh daerah pemilihan kepada individu, partai, atau lembaga untuk bertindak sebagai perwakilan mereka.[1] Konsep pemerintah memiliki mandat sah untuk memerintah melalui kemenangan yang adil dalam pemilihan umum…
2003 single by the Chemical Brothers For the concept from the fictional Dune universe, see Golden Path (Dune). The Golden PathSingle by the Chemical Brothers featuring the Flaming Lipsfrom the album Singles 93–03 B-sideNude NightReleased15 September 2003 (2003-09-15)Length4:47LabelFreestyle DustVirginAstralwerksSongwriter(s)Tom RowlandsEd SimonsWayne Michael CoyneSteven Gregory DrozdProducer(s)The Chemical BrothersThe Chemical Brothers singles chronology Come with Us/The Tes…
East VenturesJenisModal venturaDidirikan2009KantorpusatJakarta, Singapura, TokyoWilayah operasiKanada, Hong Kong, India, Indonesia, Jepang, Malaysia, Selandia Baru, Singapura, Thailand, Amerika Serikat, VietnamTokohkunci Willson Cuaca (Founding Partner) Batara Eto (Founding Partner) Taiga Matsuyama (Founding Partner) Roderick Purwana (Managing Partner) Koh Wai Kit (Managing Partner) Shinichiro Hori (Partner) Melisa Irene (Partner) David Fernando Audy (Operating Partner) Triawan Munaf (Venture Ad…
Far-right anti-Islam movement Counter-jihad, also known as the counter-jihad movement,[1] is a self-titled political current loosely consisting of authors, bloggers, think tanks, street movements and campaign organisations all linked by beliefs that view Islam not as a religion but as an ideology that constitutes an existential threat to Western civilization. Consequently, counter-jihadists consider all Muslims as a potential threat, especially when they are already living within Western…
Realismo direto e indireto é um conceito filosófico. Nota: Para movimento artístico e literário, veja Realismo. Nós percebemos o mundo externo como ele realmente é? A questão do realismo direto ou ingênuo, em oposição ao indireto ou realismo representacional, surge na filosofia da percepção e da mente para fora do debate sobre a natureza da experiência consciente. A questão epistemológica de que se o mundo que vemos ao nosso redor é o mundo real em si ou simplesmente uma pe…
غالبا ما تدرس النيازك كجزء من الكيمياء الكونية. علم الكيمياء الكونية (بالإنجليزية: chemical cosmology) هو دراسة التركيب الكيميائي للمادة في الكون والعمليات التي أدت إلى تلك التراكيب.[1] وتغطي دراسة علم الكيمياء الكونية العناصر والمركبات الكيميائية والفلزات ومجمل العمليات الكي…
Island in the Grenadines BequiaBequiaShow map of Saint Vincent and the GrenadinesBequiaShow map of Lesser AntillesBequiaShow map of CaribbeanGeographyLocationCaribbeanCoordinates13°0′N 61°14′W / 13.000°N 61.233°W / 13.000; -61.233Area7 sq mi (18 km2)AdministrationSaint Vincent and the GrenadinesDemographicsPopulationabout 5,300Ethnic groupsAfrican, Scottish and CaribAdditional informationBequia Marine Conservation AreaIUCN category VI (protected are…
Lokasi Pengunjung: 3.15.214.76