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enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general
Steiner's_conic_problem
Topics referred to by the same term
mathematics, Steiner's problem (named after Jakob Steiner) may refer to: Steiner's calculus problem The Steiner tree problem Steiner's conic problem This disambiguation
Steiner's_problem
Curve from a cone intersecting a plane
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola
Conic_section
Swiss mathematician (1796–1863)
symmetrization Steiner system Steiner surface Steiner conic Steiner's conic problem Steiner's problem Steiner tree Steiner chain Poncelet–Steiner theorem Parallel
Jakob_Steiner
Plane curve: conic section
The earliest known work on conic sections was by Menaechmus in the 4th century BC. He discovered a way to solve the problem of doubling the cube using
Parabola
Problem in algebraic geometry
principal applications are the solutions to problems in enumerative geometry (e.g., Steiner's conic problem) and the derivation of the multiple-point formula
Residual_intersection
French mathematician (1793–1880)
Spherical Conics, adding a significant amount of original material. Jakob Steiner had proposed Steiner's conic problem of enumerating the number of conic sections
Michel_Chasles
Natural number
prime quadruplet set 3264 – solution to Steiner's conic problem: number of smooth conics tangent to 5 given conics in general position 3266 – sum of first
3000_(number)
Principle in geometry
conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that
Five_points_determine_a_conic
Method of drawing geometric objects
non-constructivity of conics. If the initial conic is considered as a given, then the proof must be reviewed to check if other distinct conics need to be generated
Straightedge and compass construction
Straightedge_and_compass_construction
Geometric shape
degenerate conics, which require considering the cylindrical conics. According to G. B. Halsted, a cone is generated similarly to a Steiner conic only with
Cone
Plane curve: conic section
hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the
Hyperbola
Geometry problem about finding touching circles
solutions to the problem. Every quadratic equation in X, Y, and Z determines a unique conic, its vanishing locus. Conversely, every conic in the complex
Problem_of_Apollonius
Unique ellipse tangent to all 3 midpoints of a given triangle's sides
midpoints. There is no other (non-degenerate) conic section with the same properties, because a conic section is determined by 5 points/tangents. b)
Steiner_inellipse
Topics referred to by the same term
six points on a conic; see Pascal's theorem § Hexagrammum Mysticum Steiner tree problem, an algorithmic problem of finding extra Steiner points to add to
Steiner_point
Theorem of 2D geometry
as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite
Poncelet's_closure_theorem
Overview of and topical guide to geometry
Compass and straightedge constructions Squaring the circle Complex geometry Conic section Focus Circle List of circle topics Thales' theorem Circumcircle
Outline_of_geometry
Universality of construction using just a straightedge and a single circle with center
sides three non-intersecting circles not all in the same coaxial system any conic section with its foci (or with the center and one focus) Given only two
Poncelet–Steiner_theorem
Set of circles related by tangency
transformed bounding circles. The centers of the circles of a Steiner chain lie on a conic section. For example, if the smaller given circle lies within
Steiner_chain
Mathematical proposition or corollary
developed projective geometry of conics. Look up porism in Wiktionary, the free dictionary. Poncelet's porism Steiner's porism Eves, Howard W. (1995). College
Porism
Plane curve
method to construct single points of an ellipse relies on the Steiner generation of a conic section: Given two pencils B ( U ) , B ( V ) {\displaystyle
Ellipse
French polymath (1623–1662)
projective geometry; he wrote a significant treatise on the subject of conic sections at the age of 16. He later corresponded with Pierre de Fermat on
Blaise_Pascal
American mathematician
figurative point. Halsted uses the approach of a Steiner conic in article 77 for the definition of a conic: "If two coplanar non-copunctual flat pencils
G._B._Halsted
British church minister and mathematician (1806–1895)
points of opposite sides of a hexagon inscribed within a conic section. Any six points on a conic may be joined into a hexagon in 60 different ways, forming
Thomas_Kirkman
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Sand-Reckoner). Apollonius of Perga, in his extant work Conics, refined and developed the theory of conic sections that was first outlined by Menaechmus, Euclid
Ancient_Greek_mathematics
4th-century Greek mathematician (c. 290–350)
ratio to its distance from a given straight line is a conic, and is followed by proofs that the conic is a parabola, ellipse, or hyperbola according as the
Pappus_of_Alexandria
Geometric treatise by Archimedes
no easy means to find the area of a conic section. Archimedes provides the first attested solution to this problem by focusing specifically on the area
Quadrature_of_the_Parabola
American mathematician
analyzed the propagation of singularities for solutions of wave equation on conic manifolds with Richard B. Melrose and later on edge manifolds with Richard
Jared_Wunsch
(mathematics) Bernoulli's quadrisection problem Brocard circle Brocard points Brocard triangle Carnot's theorem (conics) Carnot's theorem (inradius, circumradius)
List_of_triangle_topics
French engineer and mathematician (1788–1867)
conjugates; relating these to the poles and polar lines associated with conic sections. He developed the concept of parallel lines meeting at a point
Jean-Victor_Poncelet
made significant advances to the study of conic sections, showing that one can obtain all three varieties of conic section by varying the angle of the plane
History_of_mathematics
Probability distribution
ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English
Normal_distribution
Polynomial equation of degree 3
are believed to have come close to solving the problem of doubling the cube using intersecting conic sections, though historians such as Reviel Netz
Cubic_equation
Mathematical transform that expresses a function of time as a function of frequency
are supported on the (degenerate) conic ξ2 − f2 = 0. We may as well consider the distributions supported on the conic that are given by distributions of
Fourier_transform
Shape with three sides
triangle's vertices, it has the smallest area. The Kiepert hyperbola is unique conic that passes through the triangle's three vertices, its centroid, and its
Triangle
Relative distance of a point from a circle
M'Clelland: A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation,1891, Verlag: Creative Media Partners
Power_of_a_point
Line constructed from a triangle
"Non-Euclidean Triangle Continuum" at the Wolfram Demonstrations Project Nine-point conic and Euler line generalization, A further Euler line generalization, and
Euler_line
Mathematics book
equivalences between curves. Chapters four and five concern conic sections, and the theorem that when a conic has at least one rational point it has infinitely
Diophantus and Diophantine Equations
Diophantus_and_Diophantine_Equations
Weierstrass function. Intersection theory. In 1848 Steiner claimed that the number of conics tangent to 5 given conics is 7776 = 65, but later realized this was
List_of_incomplete_proofs
Archaeological site in Iran
through VI, which are diagnostic pottery for the Uruk culture. A few small conic clay tokens were also found. Metallurgy. A notable discovery was one of
Tal-i-Iblis
Ellipse tangent to all sides of a triangle
of inellipses. The Steiner inellipse plays a special role: Its area is the greatest of all inellipses. Because a non-degenerate conic section is uniquely
Inellipse
Equation for radii of tangent circles
(2016), "The parabolic pencil – a common line element", The Universe of Conics, Springer, p. 327, doi:10.1007/978-3-662-45450-3_7, ISBN 978-3-662-45449-7
Descartes'_theorem
Relationship between fields of study
their mutual influence, the role of mathematical rigor in physics, and the problem of explaining the effectiveness of mathematics in physics. In his work
Relationship between mathematics and physics
Relationship_between_mathematics_and_physics
Dutch mathematician and physicist (1629–1695)
triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended
Christiaan_Huygens
1920 novel by F. Scott Fitzgerald
sophomore year he is "conditioned" and fails in the fall an important exam on "conic sections" , which prevents his original plan "to be one of the gods of the
This_Side_of_Paradise
French polymath (1596–1650)
many of Galileo's ideas. Together, they worked on free fall, catenaries, conic sections, and fluid statics. Both believed that it was necessary to create
René_Descartes
Arab physicist, mathematician and astronomer (c. 965 – c. 1040)
calculate the volume of a paraboloid. Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and
Ibn_al-Haytham
American mathematician
doi:10.1090/S0002-9904-1916-02895-3. Weaver, J. H. (1917). "On foci of conics". Bull. Amer. Math. Soc. 23 (8): 357–365. doi:10.1090/S0002-9904-1917-02961-8
James_Henry_Weaver
Circles tangent to all three sides of a triangle
that passes through the vertices of a triangle Circumconic and inconic – Conic section that passes through the vertices of a triangle or is tangent to
Incircle_and_excircles
Pompeiu's theorem (Euclidean geometry) Poncelet's closure theorem (conics) Poncelet–Steiner theorem (geometry) Ptolemy's theorem (geometry) Pythagorean theorem
List_of_theorems
Periodic comet
that in the past. Kepler orbit – Celestial orbit whose trajectory is a conic section in the orbital plane List of Halley-type comets The comet is known
Halley's_Comet
Algebraic curve in mathematics
factorization. An elliptic curve is not an ellipse in the sense of a projective conic, which has genus zero: see elliptic integral for the origin of the term
Elliptic_curve
American mathematician
ISBN 978-3-540-18360-0. Grosshans, F. D. (1 June 1981). "Rigid Motions of Conics: an Introduction to Invariant Theory". The American Mathematical Monthly
Frank_Grosshans
1990 single by Madonna
Lourdes Leon. During the performance Madonna wears a new version of the conic bra, consisting of a black cone mini dress, encrusted with black crystals
Vogue_(song)
Mathematical space with a notion of distance
domains bounded by a conic in a projective space. His distance was given by logarithm of a cross ratio. Any projectivity leaving the conic stable also leaves
Metric_space
List of definitions of terms and concepts commonly used in aerospace engineering
the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Period of eastern Mediterranean history from 323 to 30 BC
most characteristic product of Hellenistic mathematics was the theory of conic sections, reaching its greatest achievement in the work of Apollonius. It
Hellenistic_period
List of topics related to π Pole and polar – Unique point and line of a conic section Power of a point – Relative distance of a point from a circle Radical
List_of_circle_topics
Phase in art history
Proto-Cubist artworks typically depict objects in geometric schemas of cubic or conic shapes. The illusion of classical perspective is progressively stripped
Proto-Cubism
Annual music festival that takes place near Tuttlingen, Germany
Foundation Beth Gibbons and Rustin Man Blackmail Brendan Benson Coldplay Conic Console Counting Crows Danko Jones The Datsuns Fu Manchu Goldfrapp Good
Southside_Festival
scheme X is a quasi-coherent sheaf that is finitely generated as OX-module. conic An algebraic curve of degree two. connected The scheme is connected as a
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
First edition works in Greek
Cambridge University Press, 2013, pp. 2, 330. G. J. Toomer (ed.), Apollonius: Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the
List of editiones principes in Greek
List_of_editiones_principes_in_Greek
Affine space over the complex numbers
intersects the line at infinity, whereas an ellipse does not. However, any two conic sections are projectively equivalent. So a parabola and ellipse are the
Complex_affine_space
– Benedictine who made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy, and gave the first known proof by mathematical
List of Catholic clergy scientists
List_of_Catholic_clergy_scientists
Branch of geometry
} for some τ : M → R {\displaystyle \tau :M\to \mathbb {R} } . Given a conic section in the plane, the polar reciprocation operation is an involutive
Contact_geometry
Ancient Greek spherical geometry treatise
Medieval Latin Translations (in Arabic, Latin, and English). Stuttgart: Franz Steiner. ISBN 9783515092883. Sidoli, Nathan; Thomas, Robert Spencer David, eds
Theodosius'_Spherics
Series of books published by Springer-Verlag
doi:10.1007/0-387-29052-4. ISBN 978-0-387-25530-9. Bix, Robert (2006). Conics and Cubics: A Concrete Introduction to Algebraic Curves (2nd ed.). doi:10
Undergraduate Texts in Mathematics
Undergraduate_Texts_in_Mathematics
Sculptures made during the Cubist art movement
Some time after Joseph Csaky's 1911-14 sculptural figures consisting of conic, cylindrical and spherical shapes, a translation of two-dimensional form
Cubist_sculpture
World War II signals intelligence agency of the German Luftwaffe
aerial poles bent upward on each end greatly improved reception. In addition conic and mattress-type aerials were tried out. In spite of these experiments
Luftnachrichten_Abteilung_350
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
Surname or Lastname
English
English : occupational name for a stonemason or stonecutter, or a topographic name for someone who lived on stony ground, from a derivative of Middle English stene ‘stony place’. Compare Stone.
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
Surname or Lastname
English
English : patronymic from Steer.
Surname or Lastname
English
English : of uncertain origin; possibly a topographic name for someone who lived where wormwood (Artemesia absinthium) grew, Middle English wormod, or a metonymic occupational name for a herbalist. In the Middle Ages wormwood was variously used as a tonic and vermifuge, in brewing ale, and to protect clothes and linen from moths and fleas.
Surname or Lastname
English
English : patronymic from Wick 2, or variant of the habitational name Wick, with genitive or plural -s. There has been much confusion between this name and Weeks.In 1638 Richard Wickes (also known as Richard Atwick), of Staines, Middlesex, England, died, leaving a bequest to “my son John Wickes now living in New England.†This John Wickes came from London, England, to Plymouth, MA, in 1635, and subsequently settled at Portsmouth, RI.
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Surname or Lastname
English
English : from Old English stÄn ‘stone’, in any of several uses. It is most commonly a topographic name, for someone who lived either on stony ground or by a notable outcrop of rock or a stone boundary-marker or monument, but it is also found as a metonymic occupational name for someone who worked in stone, a mason or stonecutter. There are various places in southern and western England named with this word, for example in Buckinghamshire, Gloucestershire, Hampshire, Kent, Somerset, Staffordshire, and Worcestershire, and the surname may also be a habitational name from any of these.Translation of various surnames in other languages, including Jewish Stein, Norwegian Steine, and compound names formed with this word.This name was brought independently to New England by many bearers from the 17th century onward. Thomas Scott was one of the founders of Hartford, CT, (coming from Cambridge, MA, with Thomas Hooker) in 1635.
Surname or Lastname
English
English : habitational name from a place on the Thames west of London, apparently named with the plural of Old English stÄn ‘stone’. The reference may be to milestones on the Roman road that ran through the town.
Girl/Female
American, Arabic, Australian, British, Chinese, English
Stone of the Colic; The Gemstone Jade; Green in Colour
Boy/Male
Australian, Danish, Norwegian, Swedish
Stone Fighter
Girl/Female
Gujarati, Hindu, Indian, Marathi, Telugu
Sunrise; Comic
Surname or Lastname
English (Sussex)
English (Sussex) : topographic name for someone who lived in a stone-built house (see Stone), with the habitational or agent suffix -er.Translation of German Steiner.
Girl/Female
Indian, Telugu
Destroyer of Problems
Surname or Lastname
English
English : variant of Stevens.
Boy/Male
Hindu, Indian
Problem
Boy/Male
Muslim
Problem solver
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Boy/Male
German
Sone.
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
Male
Turkish
Turkish unisex name DUYGU means "emotion."
Female
Swedish
 Swedish feminine form of Old Norse Alf, ALVA means "elf." Compare with another form of Alva.
Boy/Male
Australian, Christian, Danish, Finnish, French, German, Latin
Fortunate
Girl/Female
French American Latin English
Bright.
Female
Egyptian
, the daughter of Prince Psametik.
Boy/Male
French
Woman from Magdala.
Female
Italian
Italian pet form of Latin Maria, MARIELLA means "obstinacy, rebelliousness" or "their rebellion."
Boy/Male
English
Red wolf.
Boy/Male
Tamil
Gift
Surname or Lastname
English (Midlands)
English (Midlands) : unexplained.possibly an Americanized spelling of German Minkler.
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
STEINERS CONIC-PROBLEM
n.
Ionic type.
a.
A combining form, meaning somewhat resembling a cone; as, conico-cylindrical, resembling a cone and a cylinder; conico-hemispherical; conico-subulate.
n.
Lead colic.
n.
A workman who stains; as, a stainer of wood.
n.
A tonic.
a.
Of or pertaining to tension; increasing tension; hence, increasing strength; as, tonic power.
n.
A conic section.
n.
The Ionic dialect; as, the Homeric Ionic.
a.
Alt. of Conical
a.
Of or pertaining to the colon; as, the colic arteries.
a.
Pertaining to the Ionic order of architecture, one of the three orders invented by the Greeks, and one of the five recognized by the Italian writers of the sixteenth century. Its distinguishing feature is a capital with spiral volutes. See Illust. of Capital.
n.
One of a sect or school of philosophers founded by Antisthenes, and of whom Diogenes was a disciple. The first Cynics were noted for austere lives and their scorn for social customs and current philosophical opinions. Hence the term Cynic symbolized, in the popular judgment, moroseness, and contempt for the views of others.
a.
Comic, farcical.
a.
Sourness or severity of countenance; sterness.
n.
A foot consisting of four syllables: either two long and two short, -- that is, a spondee and a pyrrhic, in which case it is called the greater Ionic; or two short and two long, -- that is, a pyrrhic and a spondee, in which case it is called the smaller Ionic.
n.
A verse or meter composed or consisting of Ionic feet.
a.
Of or pertaining to colic; affecting the bowels.
n.
Conic sections.
a.
Tonic.
n.
A tonic element or letter; a vowel or a diphthong.