Steinern.

/ˈʃtʌɪnə/

Etymology: < the name of Jakob Steiner (1796–1863), Swiss geometer.

Mathematics.

Used attributively and in the possessive to designate various mathematical concepts suggested by Steiner.

a. Steiner triple or triplet system (see quot. 1939); so Steiner triplet; also Steiner system, a generalization of the triple system to other numbers (see quot. 1974¹). [Steiner first described such systems in Jrnl. f. d. reine u. angewandte Math. (1853) XLV. 181.]

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set

set1857

interval1902

intersection1909

union1912

lattice1933

matroid1935

closure1937

Steiner triple or triplet system1939

recursive set1943

convex hull1951

power set1953

convex envelope1964

Steiner system1966

Julia set1976

Mandelbrot set1984

1939 R. C. Bose in Annals Eugenics IX. 354 Steiner (1853) proposed the problem of arranging N things in triplets, such that every pair occurs in just one and only one triplet. Such an arrangement may be called a simple triple system or a Steiner's triplet system.

1963 H. J. Ryser Combinatorial Math. viii. 100 The Steiner triple system of order 7 is the same as the projective plane of order 2 in the preceding chapter.

1966 Annali di Matematica LXXI. 199 The Steiner system S(5, 8, 24) is an arrangement of 24 elements in sets of 8, such that any 5 of the elements belong to exactly one set.

1974 I. Anderson First Course Combinatorial Math. vii. 102 A Steiner system S(l, m, n) is a collection of m-element subsets of an n element set B such that every l-element subset of B lies in exactly one of the m-element sets.

1974 I. Anderson First Course Combinatorial Math. vii. 102 A Steiner triple system is an S(2, 3, n) for some n.

1980 Sci. Amer. May 14/2 Since Steiner triplets are not ordered, the solution is of course unique.

b. Used with reference to the problem of finding the set of line segments of minimum total length needed to connect a given set of points in a metric space.

ΘΚΠ

the world > relative properties > number > geometry > [adjective] > of geometrical problems

quadrable1686

tetragonistic1710

tetragonistical1727

Steiner1941

1941 R. Courant & H. E. Robbins What is Math.? vii. 359 In Steiner's problem three fixed points A, B, C are given. It is natural to generalize this problem to the case of n given points.

1941 R. Courant & H. E. Robbins What is Math.? vii. 360 To find the really significant extension of Steiner's problem we must abandon the search for a single point P... Given n points..to find a connected system of straight line segments of shortest total length such that any two of the given points can be joined by a polygon consisting of segments of the system.

1961 Canad. Math. Bull. 4 143 Given a triangle T with the vertices a₁, a₂, a₃, to find in the plane of T the point p which minimizes the sum of the distances |pa₁| + |pa₂| + |pa₃|. p, called the Steiner point of T, is unique.

1968 SIAM Jrnl. Appl. Math. 16 1 A Steiner minimal tree for given points A₁, .., An in the plane is a tree which interconnects these points using lines of shortest possible total length. In order to achieve minimum length the Steiner minimal tree may contain other vertices (Steiner points) beside A₁, ..An.

1979 Sci. Amer. Apr. 37/1 First is the Steiner problem of the shortest roads linking many cities.

This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018).

单词	steiner
释义	Steinern. /ˈʃtʌɪnə/ Etymology: < the name of Jakob Steiner (1796–1863), Swiss geometer. Mathematics. Used attributively and in the possessive to designate various mathematical concepts suggested by Steiner. a. Steiner triple or triplet system (see quot. 1939); so Steiner triplet; also Steiner system, a generalization of the triple system to other numbers (see quot. 1974¹). [Steiner first described such systems in Jrnl. f. d. reine u. angewandte Math. (1853) XLV. 181.] ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set set1857 interval1902 intersection1909 union1912 lattice1933 matroid1935 closure1937 Steiner triple or triplet system1939 recursive set1943 convex hull1951 power set1953 convex envelope1964 Steiner system1966 Julia set1976 Mandelbrot set1984 1939 R. C. Bose in Annals Eugenics IX. 354 Steiner (1853) proposed the problem of arranging N things in triplets, such that every pair occurs in just one and only one triplet. Such an arrangement may be called a simple triple system or a Steiner's triplet system. 1963 H. J. Ryser Combinatorial Math. viii. 100 The Steiner triple system of order 7 is the same as the projective plane of order 2 in the preceding chapter. 1966 Annali di Matematica LXXI. 199 The Steiner system S(5, 8, 24) is an arrangement of 24 elements in sets of 8, such that any 5 of the elements belong to exactly one set. 1974 I. Anderson First Course Combinatorial Math. vii. 102 A Steiner system S(l, m, n) is a collection of m-element subsets of an n element set B such that every l-element subset of B lies in exactly one of the m-element sets. 1974 I. Anderson First Course Combinatorial Math. vii. 102 A Steiner triple system is an S(2, 3, n) for some n. 1980 Sci. Amer. May 14/2 Since Steiner triplets are not ordered, the solution is of course unique. b. Used with reference to the problem of finding the set of line segments of minimum total length needed to connect a given set of points in a metric space. ΘΚΠ the world > relative properties > number > geometry > [adjective] > of geometrical problems quadrable1686 tetragonistic1710 tetragonistical1727 Steiner1941 1941 R. Courant & H. E. Robbins What is Math.? vii. 359 In Steiner's problem three fixed points A, B, C are given. It is natural to generalize this problem to the case of n given points. 1941 R. Courant & H. E. Robbins What is Math.? vii. 360 To find the really significant extension of Steiner's problem we must abandon the search for a single point P... Given n points..to find a connected system of straight line segments of shortest total length such that any two of the given points can be joined by a polygon consisting of segments of the system. 1961 Canad. Math. Bull. 4 143 Given a triangle T with the vertices a₁, a₂, a₃, to find in the plane of T the point p which minimizes the sum of the distances \|pa₁\| + \|pa₂\| + \|pa₃\|. p, called the Steiner point of T, is unique. 1968 SIAM Jrnl. Appl. Math. 16 1 A Steiner minimal tree for given points A₁, .., An in the plane is a tree which interconnects these points using lines of shortest possible total length. In order to achieve minimum length the Steiner minimal tree may contain other vertices (Steiner points) beside A₁, ..An. 1979 Sci. Amer. Apr. 37/1 First is the Steiner problem of the shortest roads linking many cities. This entry has not yet been fully updated (first published 1986; most recently modified version published online September 2018). < n.1939
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