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Non-singular cubic surface in mathematics
mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by Clebsch (1871) and Klein
Clebsch_surface
German mathematician (1833–1872)
Elasticität fester Körper (B. G. Teubner, 1862) Clebsch graph Clebsch representation Clebsch surface Eigenvalues and eigenvectors Helmholtz equation Hyperboloid
Alfred_Clebsch
Natural number
this inequality holds for every larger n . {\displaystyle n.} The Clebsch surface has 27 exceptional lines can be defined over the real numbers. It is
27_(number)
Algebraic surface defined by a cubic polynomial
characteristic zero, smooth surfaces of degree at least 4 in P 3 {\displaystyle \mathbf {P} ^{3}} are not even uniruled. More strongly, Clebsch showed that every
Cubic_surface
One of two different regular graphs with 16 vertices
graph; it was called the Clebsch graph by Seidel (1968) because of its relation to the configuration of 16 lines on the quartic surface discovered in 1868 by
Clebsch_graph
Cayley nodal cubic surface, a certain cubic surface with 4 nodes Cayley's ruled cubic surface Clebsch surface or Klein icosahedral surface Fermat cubic Monkey
List of complex and algebraic surfaces
List_of_complex_and_algebraic_surfaces
Rational numbers with root 5 added
geometry, it is proven that every non-singular cubic surface contains exactly 27 lines. The Clebsch surface is unusual in that all 27 lines can be defined over
Golden_field
paraboloid (a ruled surface) Paraboloid Dini's surface Pseudosphere Cayley cubic Barth sextic Clebsch cubic Monkey saddle (saddle-like surface for 3 legs.) Torus
List_of_surfaces
Surface in algebraic geometry
the Cayley cubic surface, and the Clebsch diagonal surface. del Pezzo surfaces (Fano surfaces) Enneper surface Hirzebruch surfaces Σn P1×P1 The product
Rational_surface
Algebraic surface in mathematics
gives a long table of examples. The Clebsch surface blown up at its 10 Eckardt points is a Hilbert modular surface. Given a quadratic field extension K
Hilbert_modular_variety
In case of surface gravity waves, the Clebsch representation leads to a rotational-flow form of Luke's variational principle. For the Clebsch representation
Clebsch_representation
Book on objects used to teach mathematics
algebraic surfaces, including Cayley's ruled cubic surface, the Clebsch surface, Fresnel's wave surface, the Kummer surface, and the Roman surface, with commentary
Mathematical_Models_(Fischer)
in four variables. The zeros form a cubic surface in 3-dimensional projective space. Salmon (1860) and Clebsch (1861, 1861b) studied the ring of invariants
Quaternary_cubic
Mathematics of surface waves on a fluid
include surface tension effects, and by using Clebsch potentials to include vorticity. Luke's Lagrangian formulation is for non-linear surface gravity
Luke's_variational_principle
Special mathematical functions defined on the surface of a sphere
{\displaystyle q=m} , obeying all the properties of such operators, such as the Clebsch-Gordan composition theorem, and the Wigner-Eckart theorem. They are, moreover
Spherical_harmonics
German mathematician (1849–1925)
and thus became acquainted with Alfred Clebsch, who had relocated to Göttingen in 1868. Klein visited Clebsch the next year, along with visits to Berlin
Felix_Klein
(a ruled surface) Paraboloid Sphericon Oloid Dini's surface Pseudosphere See the list of algebraic surfaces. Cayley cubic Barth sextic Clebsch cubic Monkey
List_of_mathematical_shapes
16-regular graph with 27 vertices and 216 edges
subgraphs are all isomorphic to the complement graph of the Clebsch graph. Since the Clebsch graph is triangle-free, the Schläfli graph is claw-free. It
Schläfli_graph
German mathematician (1826–1866)
Jacobian variety of the Riemann surface, an example of an abelian manifold. Many mathematicians such as Alfred Clebsch furthered Riemann's work on algebraic
Bernhard_Riemann
Species of herb
with 8-12 flowers per whorl. Only a few flowers are in bloom at a time. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_roborowskii
Plant species in the mint family
Extension Gardener Plant Toolbox". plants.ces.ncsu.edu. Retrieved 2022-05-20. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_sclarea
Species of plant
inflorescences are 6–8 inches long, with the flowers growing opposite. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_scutellarioides
Cubic graph with 10 vertices and 15 edges
graph are linked. The Clebsch graph contains many copies of the Petersen graph as induced subgraphs: for each vertex v of the Clebsch graph, the ten non-neighbors
Petersen_graph
Species of flowering plant
wine-colored calyx that is covered with hairs. The plant seeds profusely. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_viscosa
Differential calculus on function spaces
Strauch[which?] (1849), John Hewitt Jellett (1850), Otto Hesse (1857), Alfred Clebsch (1858), and Lewis Buffett Carll (1885), but perhaps the most important
Calculus_of_variations
Branch of mathematics
the direct method in the calculus of variations. In the 1860s and 1870s, Clebsch, Gordan, Brill, and especially M. Noether studied algebraic functions and
Abstract_algebra
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
proven by Alfred Clebsch and Feodor Deahna. Deahna was the first to establish the sufficient conditions for the theorem, and Clebsch developed the necessary
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Motion of rigid body in ideal fluid
integration, and the dynamics of the body is described by the Kirchhoff – Clebsch equations: d d t ∂ L ∂ ω = ∂ L ∂ ω × ω + ∂ L ∂ v × v , d d t ∂ L ∂ v =
Kirchhoff_equations
which dates from 1046 BC to 256 BC. The Clebsch diagonal surface demonstrates the 27 lines on a cubic surface. Sphere eversion – that a sphere can be
Mathematical_visualization
Species of shrub
bulleyana. The flowers of S. bulleyana are purple-blue with no spotting. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_flava
Theory of subatomic structure
varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic illustrated on the right is an algebraic variety defined using a
String_theory
Every triangle-free planar graph is 3-colorable
showed that every triangle-free planar graph also has a homomorphism to the Clebsch graph, a 4-chromatic graph. By combining these two results, it may be shown
Grötzsch's_theorem
Swiss mathematician (1851–1916)
complexes. Some years before, in 1872, he constructed a model of the Clebsch's diagonal surface. Returned to Switzerland, he was mathematics professor at Ryffel
Adolf_Weiler
Unsolved problem in number theory
Browning, T. D. (2007). "An overview of Manin's conjecture for del Pezzo surfaces". In Duke, William (ed.). Analytic number theory. A tribute to Gauss and
Manin_conjecture
Species of flowering plant
specific epithet semiatra refers to the corolla tube and its two colors. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_semiatrata
German mathematician (1804–1851)
last multiplier is treated in Vorlesungen über Dynamik, edited by Alfred Clebsch (1866). He left many manuscripts, portions of which have been published
Carl_Gustav_Jacob_Jacobi
Shortest paths on a bounded deformed sphere-like quadric surface
28, 1838. French translation (1841). Jacobi, C. G. J. (2009) [1866]. A. Clebsch (ed.). Lectures on Dynamics. Translated by Balagangadharan, K. New Delhi:
Geodesics_on_an_ellipsoid
Species of flowering plant
United States Department of Agriculture (USDA). Retrieved 28 October 2015. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_argentea
Species of plant
grow in congested whorls, with 6–12 flowers on each 3–4 in inflorescence. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_corrugata
Species of plant
Ott 1995. Dweck 1997, p.15. Erowid (Cacahuaxochitl) 2007. Giroud 2000. Clebsch & Barner 2003, p. 106. Reisfield 1993, Previous Research. Ott 1996 Jenks
Salvia_divinorum
certain optimal control problems with multiple optimal solutions Legendre–Clebsch condition — second-order condition for solution of optimal control problem
List of numerical analysis topics
List_of_numerical_analysis_topics
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
varieties which are defined by the vanishing of polynomials. For example, the Clebsch cubic (see the illustration) is defined using a certain polynomial of degree
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Species of flowering plant
showy plant. The Latin specific epithet rubescens means "becoming red". Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_rubescens
Differential equation containing derivatives with respect to only one variable
integrating a non-linear system was communicated to Bertrand in 1868. Clebsch (1873) attacked the theory along lines parallel to those in his theory
Ordinary differential equation
Ordinary_differential_equation
Group of rotations in 3 dimensions
meaning that The D(ℓ) can be obtained from the D(m, n) of above using Clebsch–Gordan decomposition, but they are more easily directly expressed as an
3D_rotation_group
German mathematician (1862 – 1930)
functions are, in fact, binary forms of the type studied by Gordan and Clebsch. Über die Geometrie der Kegelschnitte insbesondere deren Charakteristikenproblem
Eduard_Study
French mathematician (1746–1818)
equation Monge patch Monge point Monge–Ampère equation Monge's theorem Clebsch representation Earth mover's distance Seconds pendulum Transportation theory
Gaspard_Monge
Concepts from linear algebra
eigenvalues of orthogonal matrices lie on the unit circle, and Alfred Clebsch found the corresponding result for skew-symmetric matrices. Finally, Karl
Eigenvalues_and_eigenvectors
Species of plant
of the World Online. Royal Botanic Gardens, Kew. Retrieved 2024-05-04. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_shannonii
Species of shrub
butterflies, insects, and hummingbirds from late spring until frost. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_melissodora
Species of shrub
have a pale lavender upper lip, and an off-white trough-shaped lower lip. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_desoleana
Certain vector fields are the sum of an irrotational and a solenoidal vector field
visualization of fluids or vector fields. Mathematics portal Physics portal Clebsch representation for a related decomposition of vector fields Darwin Lagrangian
Helmholtz_decomposition
Type of geometry
in geometry was overtaken by research on the general algebraic curve by Clebsch, Riemann, Max Noether and others, which stretched existing techniques,
Projective_geometry
Species of flowering plant
large, turning dark purple, along with the stem of the inflorescence. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_recurva
1920s books on mathematical history by Felix Klein
Structures", which discusses algebraic geometry (including contributions by Clebsch and Noether) and algebraic number theory (Kummer, Dedekind and Hilbert
Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert
Vorlesungen_über_die_Entwicklung_der_Mathematik_im_19._Jahrhundert
German mathematician and physicist
Genealogy Project". www.mathgenealogy.org. Record of Baptism, July 28th, 1801. Clebsch, Alfred (1872). "Zum Gedächtniss an Julius Plücker". Abhandlungen der Königlichen
Julius_Plücker
Property of certain dynamical systems
problems) Geodesic motion on ellipsoids Harmonic oscillator Integrable Clebsch and Steklov systems in fluids Lagrange, Euler, and Kovalevskaya tops Neumann
Integrable_system
hyperplane xi = 0 is the Clebsch cubic surface. Its intersection with any hyperplane xi = xj is Cayley's nodal cubic surface. Its dual is the Igusa quartic
Segre_cubic
Indian physicist (1915–1997)
the Clebsch-Gordan series and coefficients of SU(2) was discussed. The new approach made it possible to establish a connection between the Clebsch-Gordan
Sudhansu_Datta_Majumdar
Species of flowering plant
scabra". Red List of South African Plants. SANBI. Retrieved 2026-01-01. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_scabra
(quantum field theory) Wick's theorem (physics) Wigner–Eckart theorem (Clebsch–Gordan coefficients) Bohr–van Leeuwen theorem (physics) Crooks fluctuation
List_of_theorems
include Felix Klein, Sophus Lie, Arthur Cayley, William Hamilton, and Alfred Clebsch. By the standard trick in projective geometry, a line in 3-dimensional
Line_complex
Species of plant
Pav". Catalogue of Life. Species 2000. n.d. Retrieved January 19, 2025. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_sagittata
German mathematician
tradition of Jakob Steiner. Schröter went to (along with mathematicians Alfred Clebsch, Rudolf Lipschitz, Carl Gottfried Neumann) the Altstädtisches Gymnasium
Heinrich_Schröter
German physicist and mineralogist (1798–1895)
problem of giving mathematical expression to the conditions holding for a surface separating two crystalline media, and worked out from theory the laws of
Franz_Ernst_Neumann
ultraelliptischen Funktionen und Integrale erster und zweiter Ordnung 1866 Alfred Clebsch and Paul Gordan, Theorie der Abel'schen Functionen 1869 Karl Weierstrass
Timeline_of_abelian_varieties
Species of shrub
United States Department of Agriculture (USDA). Retrieved 28 October 2015. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_brandegeei
Species of flowering plant
Kilimanjaro in Tanzania and is described as having a strong minty aroma. Clebsch, Betsy; Barner, Carol D. (2003). The New Book of Salvias. Timber Press
Salvia_merjamie
Russian physicist and mathematician (1846–1915)
1875. He studied theoretical physics by reading works of Gabriel Lamé, Clebsch and Clausius, that made a significant impact on the originality of his
Nikolay_Umov
Species of flowering plant
testing. Those tests also indicated S. tingitana to be a unique species. Clebsch, Betsy; Carol D. Barner (2003). The New Book of Salvias. Timber Press.
Salvia_tingitana
in the development of modern differential geometry. Milestones include (Clebsch, 1866), (Frobenius, 1877), (Darboux, 1882), (Cartan, 1899). See integrability
Pfaffian_constraint
Turkish-American theoretical physicist (1926–1994)
Moment Interactions#1962 Virtual Particles 1976 Some New Identities of the Clebsch–Gordan Coefficients and Representation Functions of So(2,1) and So(4) 1979
Asım_Orhan_Barut
Method to choose coordinate systems
a Kramers-Moyal-van-Kampen expansion of the Master equation (using the Clebsch–Gordan coefficients for decomposing tensor products)[citation needed].
Coordinate_conditions
Mathematical structure in differential geometry
– via HathiTrust. Jacobi, Carl Gustav Jakob (1884). Borchardt, C. W.; Clebsch, A. (eds.). Vorlesungen über Dynamik, gehalten an der Universitäit zu Königsberg
Poisson_manifold
inequality Clean And Environmentally Safe Advanced Reactor Clearing factor Clebsch–Gordan coefficients Clemens C. J. Roothaan Clemens Timpler Clement John
Index_of_physics_articles_(C)
Icelandic mathematician (1877–1957)
upon the earlier works of Zeuthen and other scientists, such as Rudolph Clebsch, Guido Castelnuevo and Luigi Cremona. In 1909, he submitted his thesis
Ólafur_Daníelsson
CLEBSCH SURFACE
CLEBSCH SURFACE
Female
English
 English name derived from the flower name which originally meant "a line of verse engraved on the inner surface of a ring," but later acquired the POSY means "bouquet, flower." Pet form of English Josephine, meaning "(God) shall add (another son)."Â
Surname or Lastname
English
English : topographic name for someone who lived beside a stream, from Old English læcc, læce (see Leach) + the suffix -er denoting an inhabitant.English : unflattering nickname for a lecher, Middle English lech(o)ur (Old French leceor). Reaney comments: ‘The surname is rare, probably usually disguised as Leger’.German (Letscher) : habitational name for someone from Letsch, near Bensberg, Rhineland, or various other places such as Letsche, Letschin, Letschow, etc. See also Letsch.
Girl/Female
American, Assamese, British, Celebrity, English, Gujarati, Hindu, Indian, Kannada, Malayalam, Sindhi, Telugu
A Small; Natural Hollow on the Surface of the Body; Happy; Dimples
Surname or Lastname
English
English : occupational name for a sheepshearer or someone who used shears to trim the surface of finished cloth and remove excess nap, from Middle English shereman ‘shearer’.Americanized spelling of German Schuermann.Jewish (Ashkenazic) : occupational name for a tailor, from Yiddish sher ‘scissors’ + man ‘man’.Roger Sherman (1722–93), the only man to sign all three documents at the foundation of the American republic (the Declaration of Independence, the Articles of Confederation, and the U.S. Constitution), was born in Newton, MA, a descendant of Capt. John Sherman, who had emigrated in about 1636 to MA from Dedham, Essex, England, where his father was a farmer, following his brother Edmund, who had emigrated two years earlier. A descendant of Edmund Sherman was the U.S. general William Tecumseh Sherman (1820–91), who led the Union march through GA. He was born in Lancaster, OH, the son of a judge; his middle name was bestowed in honor of a Shawnee chieftain.
Surname or Lastname
Jewish (Ashkenazic)
Jewish (Ashkenazic) : occupational name from Yiddish tesler ‘carpenter’. Compare Tesler.German : variant of Teschner.English : from an agent derivative of Old English tǣsel ‘teasel’, hence an occupational name for someone whose job was to brush the surface of newly-woven cloth or to card wood preparatory to spinning, using the dry seed-heads of teasels (a kind of thistle).
Boy/Male
Indian, Sanskrit
Surface of the Earth
Boy/Male
Hindu, Indian
Greenery; The Lush Greenery on the Surface of the Earth
Boy/Male
Australian, Chinese, Dutch, Portuguese
Silver Voice; Hell's Door; Slanting Surface
Surname or Lastname
English
English : habitational name from a place in Wiltshire named Clench, from Old English clenc ‘lump’, ‘hill’, which seems also to have been used of a patch of dry raised ground in fenland surroundings. In some cases the surname may be of topographic origin.English : metonymic occupational name for a maker or fixer of bolts and rivets, from Middle English clinch, clench ‘door nail secured by riveting or clinching’, from clench(en) ‘to fix firmly’.
Surname or Lastname
English
English : occupational name for a stone- or bricklayer, from Middle English setter ‘one who lays stones or bricks in building’ (agent derivative of setten ‘to set’).English : occupational name from Old French saietier ‘silk weaver’ (an agent derivative of sayete, a kind of silk).English : from an agent derivative of Middle English setten ‘to place (decoration, on a garment or metal surface)’, probably an occupational name for an embroiderer.German : unexplained.Norwegian : unexplained.
Boy/Male
Australian, French, German, Italian, Latin, Portuguese, Swiss
Italian Form of Paul; Small; Slanting Surface; Clear
Male
Portuguese
Portuguese name derived from the name of a Dutch town, from Middle Dutch helldinge, HÉLDER means "slanting surface."
Male
Portuguese
Variant spelling of Portuguese Hélder, ÉLDER means "slanting surface."
Surname or Lastname
Dutch and German
Dutch and German : from a Germanic personal name, Halidher, composed of the elements halið ‘hero’ + hari, heri ‘army’, or from another personal name, Hildher, composed of the elements hild ‘strife’, ‘battle’ + the same second element.Dutch and North German : topographic name for someone living on a slope, from Middle Dutch helldinge ‘slanting surface’. Compare Halder.English : from an agent derivative of Old English healdan ‘to hold’, hence a name denoting an occupier or tenant. Compare Holder.English : variant of Hilder.English : possibly a variant of Elder, with the addition of an inorganic initial H-.
Boy/Male
Tamil
Means greenery. the lush greenery on the surface of the earth
Boy/Male
Hindu
Means greenery. the lush greenery on the surface of the earth
CLEBSCH SURFACE
CLEBSCH SURFACE
Girl/Female
Bengali, Indian, Tamil, Telugu
Winner; Winning
Girl/Female
African, Arabic, Australian, French, Hebrew, Muslim, Swahili
Flower; Beauty; Star
Boy/Male
Hindu, Indian
Name of Yamadharma
Girl/Female
American, British, Christian, English, Italian
A Carved Gem Portrait; Skin
Boy/Male
Indian
Fame of God
Surname or Lastname
English
English : topographic or habitational name, from a derivative of Wick.
Girl/Female
Indian, Modern, Sikh
All True
Boy/Male
Swedish
Son of Ander.
Girl/Female
Australian, Czech, Danish, German
Peace
Girl/Female
Muslim
Light bringer
CLEBSCH SURFACE
CLEBSCH SURFACE
CLEBSCH SURFACE
CLEBSCH SURFACE
CLEBSCH SURFACE
v. t.
To give a surface to; especially, to cause to have a smooth or plain surface; to make smooth or plain.
n.
One of the minute papillary processes on certain vascular membranes; a villosity; as, villi cover the lining of the small intestines of many animals and serve to increase the absorbing surface.
a.
Having a brilliantly polished surface, as some leaves.
a.
Of or pertaining to that surface of a carpel, petal, etc., which faces toward the center of a flower.
n.
A viscid liquid, consisting of a solution of resinous matter in an oil or a volatile liquid, laid on work with a brush, or otherwise. When applied the varnish soon dries, either by evaporation or chemical action, and the resinous part forms thus a smooth, hard surface, with a beautiful gloss, capable of resisting, to a greater or less degree, the influences of air and moisture.
n.
To lay varnish on; to cover with a liquid which produces, when dry, a hard, glossy surface; as, to varnish a table; to varnish a painting.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
n.
A form of machine for dressing the surface of wood, metal, stone, etc.
v. t.
To work over the surface or soil of, as ground, in hunting for gold.
a.
Having the surface covered with a fine and dense silky pubescence; velvety; as, a velutinous leaf.
n.
A ridge or streak rising above the surface, as of cloth; hence, the texture of cloth.
n. & v. t.
See Clinch.
n.
A liquid composition applied to a gilded surface to give luster to the gold.
n.
A small bladderlike body in the substance of vegetable, or upon the surface of a leaf.
a.
Of or pertaining to the lower side or surface of a creeping moss or other low flowerless plant. Opposed to dorsal.
n.
The exterior part of anything that has length and breadth; one of the limits that bound a solid, esp. the upper face; superficies; the outside; as, the surface of the earth; the surface of a diamond; the surface of the body.
n.
A small convex hollow prominence on the surface of a shell or a coral.
imp. & p. p.
of Surface
n.
Gold powder for covering varnished surfaces.
n.
A magnitude that has length and breadth without thickness; superficies; as, a plane surface; a spherical surface.