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Every knot or link can be represented as a closed braid
In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends
Alexander's_theorem
Gives necessary and sufficient conditions for two braids to have equivalent closures
given by Alexander's theorem which states that every knot or link in three-dimensional Euclidean space is the closure of a braid. The Markov theorem, proved
Markov_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Group whose operation is a composition of braids
represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of
Braid_group
Theorem in topology
In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides
Jordan_curve_theorem
Theorem in physical cosmology
The Borde–Guth–Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout
Borde–Guth–Vilenkin_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Theorem in differential topology
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no
Hairy_ball_theorem
Operation combining two oriented knots
in the n + 1-sphere for all n. This is a theorem of Morton Brown, Barry Mazur, and Marston Morse. The Alexander horned sphere is an example of a knotted
Knot_(mathematics)
Relation between genus, degree, and dimension of function spaces over surfaces
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension
Riemann–Roch_theorem
Result in algebraic geometry
analogues of the Grothendieck–Riemann–Roch theorem can be proved using the index theorem for families. Alexander Grothendieck gave a first proof in a 1957
Grothendieck–Riemann–Roch theorem
Grothendieck–Riemann–Roch_theorem
Unique knot with a crossing number of four
braid (namely, the closure of the 3-string braid σ1σ2−1σ1σ2−1), and a theorem of John Stallings shows that any closed homogeneous braid is fibered. (2)
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Prime knot named for John Horton Conway
Jones polynomial. Both knots also have the property of having the same Alexander polynomial and Conway polynomial as the unknot. The issue of the sliceness
Conway_knot
Pathological embedding of the sphere in 3D space
Schoenflies theorem did hold in 3D. Upon realizing his error, he constructed the horned sphere as a definitive counterexample. Alexander's genius was in
Alexander_horned_sphere
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
chart (i.e. a knot and its mirror image are considered equivalent). A theorem due to Horst Schubert (1919–2001) states that every knot can be uniquely
Prime_knot
Orientable surface whose boundary is a knot or link
V={\begin{pmatrix}1&-1\\0&1\end{pmatrix}}.} It is a theorem that any link always has an associated Seifert surface. This theorem was first published by Frankl and Pontryagin
Seifert_surface
Collection of subsets that generate a topology
Tychonoff's theorem, which states that the product of non-empty compact spaces is compact, has a short proof if the Alexander Subbase Theorem is used. Base
Subbase
Mathematical knot with crossing number 7
prime knots with crossing number seven. It is the fifth twist knot. Its Alexander polynomial is Δ ( t ) = 3 t − 5 + 3 t − 1 , {\displaystyle \Delta (t)=3t-5+3t^{-1}
7_2_knot
Line joining midpoints of a complete quadrilateral's 3 diagonals
are called diagonals of the complete quadrilateral. It is a well-known theorem that the three midpoints of the diagonals of a complete quadrilateral are
Newton–Gauss_line
Knot invariant
can be found in Crowell & Fox (1963). Birman 1993. Alexander 1928. Fox 1961. Kawauchi 2012, Theorem 11.5.3, p. 150. Kawauchi credits this result to Kondo
Alexander_polynomial
Theorem relating stationary processes' autocorrelations and power spectra
Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that
Wiener–Khinchin_theorem
Formula for area of a grid polygon
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points
Pick's_theorem
The Alexander–Hirschowitz theorem shows that a specific collection of k double points in the projective space Pr will impose independent types of conditions
Alexander–Hirschowitz_theorem
Mathematical invariant of a knot or link
Potts model, in statistical mechanics. Let a link L be given. A theorem of Alexander states that it is the trace closure of a braid, say with n strands
Jones_polynomial
Subset of a manifold that is a manifold itself; an injective immersion into a manifold
differential structure on S {\displaystyle S} . Alexander's theorem and the Jordan–Schoenflies theorem are good examples of smooth embeddings. There are
Submanifold
Planar maps require at most four colors
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Simplest non-trivial closed knot with three crossings
crossing number three. It is a prime knot, and is listed as 31 in the Alexander-Briggs notation. The Dowker notation for the trefoil is 4 6 2, and the
Trefoil_knot
Theorem concerning ratios of line segments
The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry
Intercept_theorem
Theorem in topology
often called Alexander's subbase theorem, is due to James Waddell Alexander II. The lemma is typically used to prove Tychonoff's theorem. If K {\displaystyle
Alexander's_subbase_lemma
Study of mathematical knots
introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Many knots were shown to be hyperbolic knots, enabling the use of geometry
Knot_theory
Describes the fundamental group in terms of a cover by two open path-connected subspaces
Seifert–Van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called Van Kampen's theorem, expresses the
Seifert–Van_Kampen_theorem
Theorem on extension of bounded linear functionals
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace
Hahn–Banach_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
On all absolute values of rational numbers
In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers Q {\displaystyle
Ostrowski's_theorem
Soviet mathematician
Soviet mathematician. Gelfond's theorem, also known as the Gelfond–Schneider theorem, is named after him. Alexander Gelfond was born in Saint Petersburg
Alexander_Gelfond
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named
Tychonoff's_theorem
Mathematical monograph on braid groups
via Alexander's theorem that every knot or link can be formed by closing off a braid, and provides the first complete proof of the Markov theorem on equivalence
Braids, Links, and Mapping Class Groups
Braids,_Links,_and_Mapping_Class_Groups
Theorem in the large deviations theory of stochastic processes
In mathematics, the Freidlin–Wentzell theorem (due to Mark Freidlin and Alexander D. Wentzell) is a result in the large deviations theory of stochastic
Freidlin–Wentzell_theorem
Extremal graph theory bound on clique-free graph edges
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given
Turán's_theorem
Invariant of mathematical knots
demonstrated using gauge theory and its cousins: Jacob Rasmussen's new proof of a theorem of Peter Kronheimer and Tomasz Mrowka, formerly known as the Milnor conjecture
Khovanov_homology
Three linked but pairwise separated rings
extending earlier listings in the 1920s by Alexander and Briggs, the Borromean rings were given the Alexander–Briggs notation "63 2", meaning that this
Borromean_rings
Relates the length of a median of a triangle to the lengths of its sides
In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the
Apollonius's_theorem
soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature. The theorem was proven in
Alexandrov's soap bubble theorem
Alexandrov's_soap_bubble_theorem
Relates the homology of two objects to the homology of their product
mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of
Künneth_theorem
Loop seen as a trivial knot
has trivial Alexander polynomial, but the Kinoshita–Terasaka knot and Conway knot (both of which have 11 crossings) have the same Alexander and Conway
Unknot
How many times curves wind around each other
corresponding to linking number. This can be seen via the Seifert–Van Kampen theorem (either adding the point at infinity to get a solid torus, or adding the
Linking_number
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
Polynomial invariant of framed links
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Bracket_polynomial
Concerns 3 circles through triples of points on the vertices and sides of a triangle
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a
Miquel's_theorem
Function of a knot that takes the same value for equivalent knots
is known to be a "complete invariant" of the knot by the Gordon–Luecke theorem in the sense that it distinguishes the given knot from all other knots
Knot_invariant
Theorem in geometry about convex sets
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two
Radon's_theorem
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
List_of_prime_knots
Injective polynomial functions are bijective
Ax–Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck
Ax–Grothendieck_theorem
Results on the surface areas and volumes of surfaces and solids of revolution
Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with
Pappus's_centroid_theorem
Knot which lies on the surface of a torus in 3-dimensional space
( p − 1 ) ( q − 1 ) . {\displaystyle g={\frac {1}{2}}(p-1)(q-1).} The Alexander polynomial of a torus knot is t k ( t p q − 1 ) ( t − 1 ) ( t p − 1 )
Torus_knot
Classifies holomorphic vector bundles over the complex projective line
direct sum of holomorphic line bundles. The theorem was proved by Alexander Grothendieck (1957, Theorem 2.1), and is more or less equivalent to Birkhoff
Birkhoff–Grothendieck_theorem
On bipartite matching and vertex cover
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Polynomials arising in knot theory
invariant and it generalizes two polynomials previously discovered, the Alexander polynomial and the Jones polynomial, both of which can be obtained by
HOMFLY_polynomial
number Unknotting problem Volume conjecture Schubert's theorem Conway's theorem Alexander's theorem List of mathematical knots and links List of prime knots
List_of_knot_theory_topics
Theorem in probability theory
The Yamada–Watanabe theorem is a result from probability theory saying that for a large class of stochastic differential equations a weak solution with
Yamada–Watanabe_theorem
Encyclopedic website dedicated to knot theory
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
The_Knot_Atlas
In a quadrilateral with all sides tangent to a circle, sums of opposite sides are equal
The Pitot theorem in geometry states that in a tangential quadrilateral the two pairs of opposite sides have the same total length. It is named after
Pitot_theorem
Knot that bounds an embedded disk in 4-space
properties are valid for topologically and smoothly slice knots: The Alexander polynomial of a slice knot can be written as Δ ( t ) = f ( t ) f ( t −
Slice_knot
On algebraic independence of logarithms
theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. Nearly fifteen years earlier, Alexander
Baker's_theorem
theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander
Dvoretzky's_theorem
Extension of Lidskii's theorem
operators. The theorem was proven in 1955 by Alexander Grothendieck. Lidskii's theorem does not hold in general for Banach spaces. The theorem should not
Grothendieck_trace_theorem
Simplest nontrivial knot link
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Hopf_link
Mathematical theorem for algebraic structure of subgroups of free products
Kurosh subgroup theorem describes the algebraic structure of subgroups of free products of groups. The theorem was obtained by Alexander Kurosh, a Russian
Kurosh_subgroup_theorem
Mathematical knot with crossing number 7
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
74_knot
In mathematics, the Ostrowski–Hadamard gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders
Ostrowski–Hadamard gap theorem
Ostrowski–Hadamard_gap_theorem
Family of mathematical knots
twist knot depend on the number n {\displaystyle n} of half-twists. The Alexander polynomial of a twist knot is given by the formula Δ ( t ) = { n + 1 2
Twist_knot
Mathematical knot with crossing number 6
orienting the curve in either direction yields the same oriented knot. The Alexander polynomial of the 63 knot is Δ ( t ) = t 2 − 3 t + 5 − 3 t − 1 + t − 2
63_knot
Theorem related to ordinary least squares
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest
Gauss–Markov_theorem
Theorem in geometry
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the
Napoleon's_theorem
One of three theorems in geometry proved by French mathematician Victor Thébault
Thébault's theorem is the name given variously to one of the geometry problems proposed by the French mathematician Victor Thébault, individually known
Thébault's_theorem
Key results in general relativity on gravitational singularities
when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Mathematical theorem in measure theory
In mathematics, the Cramér–Wold theorem or the Cramér–Wold device is a theorem in measure theory and which states that a Borel probability measure on R
Cramér–Wold_theorem
Long dense subsets of the integers contain arbitrarily large arithmetic progressions
In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured
Szemerédi's_theorem
Connected sum of two trefoil knots with opposite chirality
which is the smallest possible crossing number for a composite knot. The Alexander polynomial of the square knot is Δ ( t ) = ( t − 1 + t − 1 ) 2 , {\displaystyle
Square_knot_(mathematics)
Theorem in quantum field theory
In quantum field theory, the C-theorem states that there exists a positive real function, C ( g i , μ ) {\displaystyle C(g_{i}^{},\mu )} , depending on
C-theorem
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Three-dimensional analog of the Pythagorean theorem
In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron
De_Gua's_theorem
Notation used to describe knots based on operations on tangles
multiple polyhedra of that number exist. Conway knot Dowker notation Alexander–Briggs notation Gauss notation "Conway notation", mi.sanu.ac.rs. "Conway
Conway_notation_(knot_theory)
Complement of a knot in three-sphere
ambient space is the three-sphere no information is lost: the Gordon–Luecke theorem states that a knot is determined by its complement. That is, if K and K′
Knot_complement
On the structure of complete Riemannian manifolds of non-positive sectional curvature
In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive
Cartan–Hadamard_theorem
Mathematical notation for describing the structure of knots
counting the number of different number sequences possible in this notation. Alexander–Briggs notation Conway notation Gauss notation Dowker, C. H.; Thistlethwaite
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Every triangle with two angle bisectors of equal lengths is isosceles
The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner. It states: Every
Steiner–Lehmus_theorem
Mathematical knot with crossing number 7
under connected sum. The 71 knot is invertible but not amphichiral. Its Alexander polynomial is Δ ( t ) = t 3 − t 2 + t − 1 + t − 1 − t − 2 + t − 3 , {\displaystyle
71_knot
Link that consists of finitely many unlinked unknots
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Unlink
Soviet mathematician (1896–1982)
number of basic laws of topological duality. In 1927, he generalized Alexander's theorem to the case of an arbitrary closed set. Alexandrov and P. S. Urysohn
Pavel_Alexandrov
Property in knot theory
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Tricolorability
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Bridge_number
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
2-bridge_knot
Two interlinked loops with five structural crossings
\sigma _{1}^{2}\sigma _{2}^{2}\sigma _{1}^{-1}\sigma _{2}^{-2}.\,} Its Alexander polynomial is Δ ( t ) = t 3 / 2 − 3 t 1 / 2 + 3 t − 1 / 2 − t − 3 / 2
Whitehead_link
The mathematician Alexander Grothendieck (1928–2014) is the eponym of many things. Ax–Grothendieck theorem Birkhoff–Grothendieck theorem Brieskorn–Grothendieck
List of things named after Alexander Grothendieck
List_of_things_named_after_Alexander_Grothendieck
Interlinked multi-loop construction where cutting one loop frees all the others
Brunnian links from almost every Brunnian link. A geometric classification theorem for Brunnian links was given. More interestingly, a canonical geometric
Brunnian_link
Invariant of framed knots
Flype Mutation Reidemeister move Skein relation Tabulation Other Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered
Self-linking_number
One of three types of isotopy-preserving local changes to a knot diagram
link diagram. Kurt Reidemeister (1927) and, independently, James Waddell Alexander and Garland Baird Briggs (1926), demonstrated that two knot diagrams belonging
Reidemeister_move
Connected sum of two trefoil knots with same chirality
square knot, the granny knot is not a ribbon knot or a slice knot. The Alexander polynomial of the granny knot is Δ ( t ) = ( t − 1 + t − 1 ) 2 , {\displaystyle
Granny_knot_(mathematics)
ALEXANDERS THEOREM
ALEXANDERS THEOREM
Girl/Female
Australian, French, Greek, Latin
Defender of Mankind; Feminine of Alexander
Boy/Male
Swedish American Greek Biblical Shakespearean
Defender of man.
Male
Romanian
Romanian form of Greek Alexandros, ALEXANDRU means "defender of mankind."
Female
English
Variant spelling of Latin Alexandria, ALEXANDREA means "defender of mankind."
Male
Dutch
, defender of man.
Male
English
Great Protector
Male
Greek
(ἈλεξανδÏεÏÏ‚) Greek name ALEXANDREUS means "from Alexandria." In the bible, this is the name of a resident of Alexandria in Egypt.
Boy/Male
American, Basque, British, Christian, Danish, Dutch, English, Finnish, French, German, Greek, Hindu, Indian, Irish, Jamaican, Latin, Netherlands, Polish, Portuguese, Shakespearean, Swedish, Swiss, Tamil, Ukrainian
Helper and Defender of Mankind; Protector of Mankind; Warrior; Defender of Men
Girl/Female
American, Australian, British, Christian, Czechoslovakian, Danish, Dutch, English, Finnish, French, German, Greek, Indian, Jamaican, Portuguese, Swedish
Protector of Man; Man's Defender; Feminine of Alexander; Helper and Defender of Mankind; To Defend; To Help
Female
Greek
 Feminine form of Greek Alexandros, ALEXANDRA means "defender of mankind."
Boy/Male
American, Australian, Chinese, French, German, Greek, Latin, Swiss
French Form of Alexander
Male
Esperanto
Esperanto form of Latin Alexandrus, ALEXANDRO means "defender of mankind."
Girl/Female
Australian, Greek, Romanian
Defender of Mankind; Similar to Alexandra and Alexander
Female
English
 Feminine form of English Alexander, ALEXANDRA means "defender of mankind." Compare with other forms of Alexandra.
Girl/Female
American, Australian, British, Chinese, Christian, Egyptian, English, Greek, Latin
Defender of Mankind; Female Version of Alexander
Male
English
(Hebrew ×Ö²×œÖ¶×›Ö°Ö¼×¡Ö·× Ö°×“Ö¶×¨): Anglicized form of Latin Alexandrus (Greek Alexandros), ALEXANDER means "defender of mankind." In the New Testament bible, this is the name of a son of Simon, a relative of the high priest, a Jew in Acts 19:33, and a coppersmith who opposed Paul.
Girl/Female
English Greek American
Feminine of Alexander. Defender of mankind.
Boy/Male
Greek American
Defender; protector of mankind. Famous Bearer: Alexander the Great.
Male
French
French and Galician-Portuguese form of Latin Alexandrus, ALEXANDRE means "defender of mankind."
Boy/Male
Greek
Defender of man.
ALEXANDERS THEOREM
ALEXANDERS THEOREM
Boy/Male
Hindu, Indian, Traditional
Man-lion
Surname or Lastname
English, Norwegian, and Danish
English, Norwegian, and Danish : variant of Lund.
Boy/Male
Hindu, Indian
Flying Up
Boy/Male
Hindu, Indian, Punjabi, Sikh
The Brave One
Girl/Female
Spanish
Hope.
Female
English
English name derived from the vocabulary word, lily, LILY means simply "lily flower."Â
Boy/Male
Hindu, Indian
One who is Near; Faith; Dignity
Boy/Male
Arthurian Legend
Name of a king.
Boy/Male
Hindu
Horse rider, A star
Boy/Male
Muslim
Conqueror. Victorious.
ALEXANDERS THEOREM
ALEXANDERS THEOREM
ALEXANDERS THEOREM
ALEXANDERS THEOREM
ALEXANDERS THEOREM
n.
That which is considered and established as a principle; hence, sometimes, a rule.
n.
One of a sect of philosophers, said to have been found in India by Alexander the Great, who went almost naked, denied themselves the use of flesh, renounced bodily pleasures, and employed themselves in the contemplation of nature.
n.
A brief writing formed as if to be inscribed on a monument, as that concerning Alexander: "Sufficit huic tumulus, cui non sufficeret orbis."
v. t.
To formulate into a theorem.
n.
An umbelliferous plant, the common Alexanders of Western Europe (Smyrnium Olusatrum).
n.
A genus of plants, some species of which produce beautiful and fragrant flowers; Cape jasmine; -- so called in honor of Dr. Alexander Garden.
n.
The dialect, formed with slight variations from the Attic, which prevailed among Greek writers after the time of Alexander.
n.
Alt. of Alisanders
n.
A name given to two species of the genus Smyrnium, formerly cultivated and used as celery now is; -- called also horse parsely.
n.
One who constructs theorems.
n.
A period of time reckoned from some particular date or epoch; a succession of years dating from some important event; as, the era of Alexander; the era of Christ, or the Christian era (see under Christian).
n.
A numerical coefficient in any particular case of the binomial theorem.
v. t.
To pass over; as, Alexander transpassed the river.
n.
A statement of a principle to be demonstrated.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
n.
A deed or act; especially, a heroic act; a deed of renown; an adventurous or noble achievement; as, the exploits of Alexander the Great.
a.
Alt. of Theorematical
a.
Theorematic.