| 单词 |
Steiner |
| 释义 |
Steiner Math.|ˈʃtaɪnə(r)|
The name of Jakob Steiner (1796–1863), Swiss geometer, used attrib. and in the possessive to designate various mathematical concepts suggested by him: 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. 1974). [Steiner first described such systems in Jrnl. f. d. reine u. angewandte Math. (1853) XLV. 181.]
1939R. 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. 1963H. 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. 1966Annali 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. 1974I. 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. Ibid., A Steiner triple system is an S(2, 3, n) for some n. 1980Sci. 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.
1941Courant & 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. Ibid. 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. 1961Canad. Math. Bull. IV. 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 {vb}pa1{vb} + {vb}pa2{vb} + {vb}pa3{vb}. p, called the Steiner point of T, is unique. 1968SIAM Jrnl. Appl. Math. XVI. 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. 1979Sci. Amer. Apr. 37/1 First is the Steiner problem of the shortest roads linking many cities. |
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单词 Steinerian 释义 Steinerian, a. and n. Math.|stanrn|[f. Steiner (see prec.) + -ian.]a.......