| 单词 | jordan curve |
| 释义 | > as lemmasJordan curve Jordan curve, any curve that is topologically equivalent to a circle, i.e. is closed and does not cross itself; so Jordan('s) (curve) theorem, the theorem that any Jordan curve in a plane divides the plane into just two distinct regions having the curve as their common boundary. ΘΚΠ the world > relative properties > number > geometry > shape or figure > [noun] > two-dimensional > closed curve oval1570 hysteresis loop1892 Jordan curve1900 the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem pons asinorum1718 Fermat's theorem1845 Bernoulli's theorem1865 Fermat's last theorem1865 Fourier's theorem1880 remainder theorem1886 Stokes' theorem1893 Jordan('s) (curve) theorem1900 Waring's theorem1920 Gödel's theorem1933 maximin1953 incompleteness theorem1955 Schwarz inequality1955 1900 W. F. Osgood in Trans. Amer. Math. Soc. 1 310 By a Jordan curve is meant a curve of the general class of continuous curves without multiple points, considered by Jordan, Cours d'Analyse, vol. I, 2d edition, 1893, p. 90. 1919 Ann. Math. 21 180 (heading) A proof of Jordan's theorem about a simple closed curve. 1939 M. H. A. Newman Elem. Topol. Plane Sets of Points vi. 132 Theorem 2·3. (Jordan's Theorem for a polygon.) A simple polygon determines two domains, of each of which it is the frontier. 1947 R. Courant & H. E. Robbins What is Math.? (ed. 4) v. 246 The Jordan curve theorem is quite simple to prove for the reasonably well-behaved curves, such as polygons or curves with continuously turning tangents, which occur in most important problems. 1965 S. Barr Exper. Topol. i. 13 A Jordan curve can be drawn on the side of the torus and still divide it into two, but not if it circles, or goes through the hole. < as lemmas |
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