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'''Separation theorem''' may refer to several theorems in different fields. ...the number of mutual funds is smaller than the number of individual assets in the portfolio. ...

{{short description|Extension of the Schwarz lemma for hyperbolic geometry}} ...[[Schwarz lemma]] for [[hyperbolic geometry]], such as the [[Poincaré half-plane model]]. ...

{{Short description|Concept in geometry}} ...by the two [[ray (geometry)|rays]] between the vertex and each [[endpoint (geometry)|endpoint]] of the segment. ...

...n [[Moritz Pasch]],<ref>{{Harvnb|Pasch|1912}}</ref> is a result in [[plane geometry]] which cannot be derived from [[Euclid's postulates]]. ...var|b}}, {{mvar|d}}).<ref>{{harvtxt|Coxeter|1969|p=179}} states the result in 12.274 but does not refer to it specifically as Pasch's theorem.</ref>}} [H ...

...ription|The 3 long diagonals of a hexagon tangent to a conic section meet in a single point}} ...n]], its principal [[diagonal]]s (those connecting opposite vertices) meet in a single point. It is named after [[Charles Julien Brianchon]] (1783–1864). ...

In [[mathematics]], a '''classification theorem''' answers the [[classificatio ...p in solving it. (A combination of invariant values is realizable if there in fact exists an object whose invariants take on the specified set of values) ...

...a geometrical space invariant under the [[symmetry group]] of that space. In more recent times, the meaning has been broadened to include a view of inva ...rofton formula|classic theorem of Crofton]] expressing the [[length]] of a plane [[curve]] as an [[expected value|expectation]] of the number of intersectio ...

...sor product]]s of [[module (mathematics)|modules]]|Homological conjectures in commutative algebra}} ...'}} must also be incident. An intersection theorem is not necessarily true in all projective geometries; it is a property that some geometries satisfy bu ...

{{short description|Gives the average curvature of any closed convex plane curve}} {{About|the concept in geometry|the concept in [[mathematical optimization]]|Fenchel's duality theorem}} ...

{{short description|One of several theorems in different areas of mathematics}} ...ry]], '''Schur's theorem''' is a theorem of [[:de:Axel Schur|Axel Schur]]. In [[functional analysis]], '''Schur's theorem''' is often called [[Schur's pr ...

In [[mathematics]], '''Weber's theorem''', named after [[Heinrich Martin Weber * {{cite book | author=Coolidge, J. L. | title=A Treatise on Algebraic Plane Curves | location=New York | publisher=Dover | page=135 | year=1959 | isbn= ...

...erential geometry]] topics. See also [[glossary of differential and metric geometry]] and [[list of Lie group topics]]. ==Differential geometry of curves and surfaces== ...

...], a smooth [[algebraic curve]] <math>C</math> in the [[complex projective plane]], of degree <math>d</math>, has [[Genus_(mathematics)#Topology|genus]] giv ...math> is any smoothly embedded connected curve representing the same class in [[homology (mathematics)|homology]] as <math>C</math>, then the genus <math ...

{{Short description|Geometry without the parallel postulate}} {{General geometry}} ...

...n lower bounds on the number of lines determined by a set of points in the plane}} ...wer bounds on the number of lines ''determined'' by a set of points in the plane. (Any line containing at least two points of point set is said to be ''dete ...

{{Short description|Geometry theorem relating to triangles}} ...ls/geometry00mois/page/233}}</ref> This theorem is given as Proposition 24 in Book I of [[Euclid's Elements|Euclid's ''Elements'']]. ...

{{short description|Theorem in hyperbolic geometry}} In [[hyperbolic geometry]], two lines are said to be '''ultraparallel''' if they do not intersect an ...

{{Short description|Theorem in plane geometry}} ...Aubel|Henricus Hubertus (Henri) Van Aubel]] (1830–1906), who published it in 1878.<ref>{{citation|last=Van Aubel|first=H.|language=French|title=Note con ...

...rve. For any algebraic curve of degree {{mvar|m}} in the real [[projective plane]], the number of components {{mvar|c}} is bounded by ...is [[Singularity theory|nonsingular]]. Moreover, any number of components in this range of possible values can be attained. ...

In [[mathematics]], a '''prime geodesic''' on a [[hyperbolic geometry|hyperbolic]] [[Surface (topology)|surface]] is a '''primitive''' [[closed g ...section presents some facts from [[hyperbolic geometry]] that are helpful in understanding prime geodesics. ...