53:
1597:
1786:
31:
1445:
1374:
1402:
1467:
1333:
1302:
1717:
1181:
1547:
281:
1820:
1770:
1671:
1281:
there are several structures that are one-dimensional spaces but are usually referred to by more specific terms. Any
247:
1410:
1572:, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.
1710:
1174:
1128:
734:
193:
1338:
1805:
1565:
17:
1149:
759:
1703:
1167:
1740:
1382:
136:
1450:
1948:
1943:
1923:
1405:
562:
242:
99:
1933:
1928:
1908:
1618:
1247:
1239:
638:
349:
227:
112:
1938:
1918:
1489:
1478:
410:
330:
325:
178:
1569:
1561:
1078:
1001:
849:
754:
276:
171:
85:
8:
2014:
1815:
1810:
1543:
1282:
1251:
1083:
1027:
940:
794:
774:
699:
589:
460:
450:
313:
188:
183:
166:
141:
129:
81:
76:
57:
1315:
2009:
1989:
1830:
1785:
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1558:
1554:
1287:
1278:
1259:
1255:
1203:
1042:
769:
609:
237:
161:
151:
122:
107:
1825:
1667:
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1113:
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879:
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663:
389:
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156:
117:
1103:
1032:
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200:
65:
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52:
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1057:
991:
839:
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1263:
1243:
1144:
1052:
996:
961:
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779:
749:
709:
614:
1639:
1118:
729:
2003:
1872:
1524:
1231:
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1123:
1108:
1037:
854:
814:
764:
539:
502:
469:
307:
303:
1892:
1857:
1750:
1305:
1062:
1011:
824:
679:
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384:
1977:
1760:
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1219:
1211:
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971:
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652:
624:
599:
35:
1689:, page 70, Cambridge Tracts in Mathematics and Mathematical Physics # 46
1972:
1852:
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is a one-dimensional space over the ring. In case the ring is an
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488:
432:
232:
1474:
1376:
is a one-dimensional space. In particular, if the field is the
1267:
1235:
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is a one-dimensional space, regardless of the dimension of the
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30:
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in which the line or curve is embedded. Examples include the
1227:
986:
910:
844:
689:
293:
288:
1695:
577:
427:
1453:
1413:
1385:
1341:
1318:
1290:
1461:
1439:
1396:
1368:
1327:
1296:
1206:in which location can be specified with a single
2001:
1586:One dimensional coordinate systems include the
1440:{\displaystyle \mathbf {P} ^{1}(\mathbb {C} )}
1711:
1175:
1666:, second edition, page 147, Academic Press
1576:Coordinate systems in one-dimensional space
1718:
1704:
1481:with respect to real-number coordinates).
1182:
1168:
51:
1640:"Пространство как математическое понятие"
1455:
1430:
1387:
29:
1507:generated by the eigenvector such that
14:
2002:
282:Straightedge and compass constructions
1699:
1548:Lie group–Lie algebra correspondence
1369:{\displaystyle \mathbf {P} ^{1}(K),}
1499:, there is a one-dimensional space
1447:is one-dimensional with respect to
24:
1538:, a one-dimensional subspace of a
1218:of which is described by a single
25:
2026:
1637:
248:Noncommutative algebraic geometry
1784:
1595:
1416:
1344:
1662:& Miron Tismenetsky (1985)
1676:
1653:
1631:
1434:
1426:
1360:
1354:
641:- / other-dimensional
13:
1:
1725:
1624:
1469:(but is sometimes called the
1397:{\displaystyle \mathbb {C} ,}
1564:over itself. Similarly, the
1462:{\displaystyle \mathbb {C} }
7:
1607:
1566:projective line over a ring
10:
2031:
1579:
1473:, as it is a model of the
1986:
1965:
1901:
1839:
1793:
1782:
1733:
1642:(in Russian). fmclass.ru
137:Non-Archimedean geometry
27:Space with one dimension
1406:complex projective line
243:Noncommutative geometry
1664:The Theory of Matrices
1619:Zero-dimensional space
1463:
1441:
1398:
1370:
1329:
1298:
1240:parametric space curve
211:Discrete/Combinatorial
38:
1490:linear transformation
1464:
1442:
1399:
1371:
1330:
1304:is a one-dimensional
1299:
1196:one-dimensional space
194:Discrete differential
33:
1902:Dimensions by number
1570:algebra over a field
1527:under the action of
1451:
1411:
1383:
1339:
1316:
1288:
1250:is called a "linear
1210:. An example is the
1544:one-parameter group
461:Pythagorean theorem
1831:Degrees of freedom
1734:Dimensional spaces
1553:More generally, a
1495:on a vector space
1459:
1437:
1394:
1366:
1328:{\displaystyle K,}
1325:
1294:
1279:algebraic geometry
1204:mathematical space
39:
1997:
1996:
1806:Lebesgue covering
1771:Algebraic variety
1582:Coordinate system
1308:over itself. The
1297:{\displaystyle K}
1238:on a plane, or a
1192:
1191:
1157:
1156:
880:List of geometers
563:Three-dimensional
552:
551:
16:(Redirected from
2022:
1794:Other dimensions
1788:
1756:Projective space
1720:
1713:
1706:
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1690:
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350:Zero-dimensional
55:
41:
40:
21:
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2000:
1999:
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1993:
1982:
1961:
1897:
1835:
1789:
1780:
1746:Euclidean space
1729:
1724:
1694:
1693:
1681:
1677:
1660:Peter Lancaster
1658:
1654:
1645:
1643:
1636:
1632:
1627:
1610:
1603:
1600:
1584:
1578:
1542:is mapped to a
1479:two-dimensional
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1448:
1429:
1420:
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1380:
1378:complex numbers
1348:
1343:
1342:
1340:
1337:
1336:
1317:
1314:
1313:
1310:projective line
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1286:
1285:
1188:
1159:
1158:
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629:
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553:
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411:Two-dimensional
402:
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372:One-dimensional
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28:
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1898:
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1895:
1890:
1885:
1883:Cross-polytope
1880:
1875:
1870:
1868:Hyperrectangle
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1860:
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1604:
1601:
1594:
1580:Main article:
1577:
1574:
1471:Riemann sphere
1457:
1436:
1432:
1428:
1423:
1418:
1393:
1389:
1365:
1362:
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1356:
1351:
1346:
1324:
1321:
1293:
1244:physical space
1190:
1189:
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615:Platonic Solid
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56:
48:
47:
26:
9:
6:
4:
3:
2:
2027:
2016:
2013:
2011:
2008:
2007:
2005:
1992:
1991:
1985:
1979:
1976:
1974:
1971:
1970:
1968:
1964:
1958:
1956:
1952:
1950:
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1925:
1922:
1920:
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1915:
1912:
1910:
1907:
1906:
1904:
1900:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1873:Demihypercube
1871:
1869:
1866:
1864:
1861:
1859:
1856:
1854:
1851:
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1848:
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1777:
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1767:
1764:
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1759:
1757:
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1738:
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1728:
1721:
1716:
1714:
1709:
1707:
1702:
1701:
1698:
1688:
1684:
1679:
1673:
1672:0-12-435560-9
1669:
1665:
1661:
1656:
1641:
1638:Гущин, Д. Д.
1634:
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1612:
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1591:
1589:
1583:
1573:
1571:
1567:
1563:
1560:
1556:
1551:
1549:
1545:
1541:
1537:
1532:
1530:
1526:
1525:invariant set
1522:
1518:
1514:
1510:
1506:
1502:
1498:
1494:
1491:
1487:
1482:
1480:
1476:
1472:
1421:
1407:
1391:
1379:
1363:
1357:
1349:
1322:
1319:
1311:
1307:
1291:
1284:
1280:
1275:
1273:
1269:
1265:
1261:
1257:
1253:
1249:
1245:
1241:
1237:
1233:
1232:ambient space
1229:
1225:
1224:straight line
1221:
1217:
1213:
1209:
1205:
1201:
1197:
1185:
1180:
1178:
1173:
1171:
1166:
1165:
1163:
1162:
1151:
1148:
1146:
1143:
1142:
1141:
1140:
1136:
1135:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1097:
1095:
1092:
1090:
1087:
1085:
1082:
1080:
1077:
1076:
1075:
1074:
1070:
1069:
1064:
1061:
1059:
1056:
1054:
1051:
1049:
1046:
1044:
1041:
1039:
1036:
1034:
1031:
1029:
1026:
1025:
1024:
1023:
1019:
1018:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
980:
978:
975:
973:
970:
968:
965:
963:
960:
958:
955:
954:
953:
952:
948:
947:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
908:
907:
906:
903:
900:
899:
889:
888:
881:
878:
876:
873:
871:
868:
866:
863:
861:
858:
856:
853:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
826:
823:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
778:
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773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
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723:
721:
718:
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713:
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708:
706:
703:
701:
698:
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693:
691:
688:
686:
683:
681:
678:
677:
669:
668:
665:
662:
661:
654:
651:
649:
646:
645:
640:
634:
633:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
601:
598:
596:
593:
591:
588:
584:
581:
580:
579:
576:
575:
572:
569:
568:
564:
558:
557:
546:
543:
541:
540:Circumference
538:
536:
533:
532:
531:
530:
527:
524:
523:
518:
515:
513:
510:
509:
508:
507:
504:
503:Quadrilateral
501:
500:
495:
492:
490:
487:
485:
482:
480:
477:
476:
475:
474:
471:
470:Parallelogram
468:
467:
462:
459:
457:
454:
452:
449:
448:
447:
446:
443:
440:
439:
434:
431:
429:
426:
424:
421:
420:
419:
418:
412:
406:
405:
398:
395:
391:
388:
386:
383:
382:
381:
378:
377:
373:
367:
366:
359:
356:
355:
351:
345:
344:
337:
334:
332:
329:
327:
324:
323:
320:
317:
315:
312:
309:
308:Perpendicular
305:
304:Orthogonality
302:
300:
297:
295:
292:
290:
287:
286:
283:
280:
279:
278:
268:
265:
264:
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228:Computational
226:
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150:
148:
145:
143:
140:
138:
135:
131:
128:
124:
121:
120:
119:
116:
115:
114:
113:Non-Euclidean
111:
109:
106:
105:
101:
95:
94:
87:
83:
80:
78:
75:
74:
72:
71:
67:
63:
59:
54:
50:
49:
46:
43:
42:
37:
32:
19:
1988:
1954:
1913:
1893:Hyperpyramid
1858:Hypersurface
1751:Affine space
1741:Vector space
1686:
1678:
1663:
1655:
1644:. Retrieved
1633:
1585:
1552:
1533:
1528:
1520:
1516:
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1500:
1496:
1492:
1483:
1306:vector space
1276:
1199:
1195:
1193:
1012:Parameshvara
825:Parameshvara
595:Dodecahedron
371:
179:Differential
1978:Codimension
1957:-dimensions
1878:Hypersphere
1761:Free module
1602:Number line
1588:number line
1540:Lie algebra
1519:, that is,
1486:eigenvector
1260:curvilinear
1256:rectilinear
1220:real number
1212:number line
1137:Present day
1084:Lobachevsky
1071:1700s–1900s
1028:Jyeṣṭhadeva
1020:1400s–1700s
972:Brahmagupta
795:Lobachevsky
775:Jyeṣṭhadeva
725:Brahmagupta
653:Hypersphere
625:Tetrahedron
600:Icosahedron
172:Diophantine
36:number line
18:1 dimension
2015:1 (number)
2004:Categories
1973:Hyperspace
1853:Hyperplane
1687:Lie Groups
1683:P. M. Cohn
1646:2015-06-06
1625:References
1614:Univariate
1559:length-one
1546:under the
1536:Lie theory
1484:For every
1226:or smooth
1208:coordinate
997:al-Yasamin
941:Apollonius
936:Archimedes
926:Pythagoras
916:Baudhayana
870:al-Yasamin
820:Pythagoras
715:Baudhayana
705:Archimedes
700:Apollonius
605:Octahedron
456:Hypotenuse
331:Similarity
326:Congruence
238:Incidence
189:Symplectic
184:Riemannian
167:Arithmetic
142:Projective
130:Hyperbolic
58:Projecting
2010:Dimension
1863:Hypercube
1841:Polytopes
1821:Minkowski
1816:Hausdorff
1811:Inductive
1776:Spacetime
1727:Dimension
1404:then the
1252:dimension
1114:Minkowski
1033:Descartes
967:Aryabhata
962:Kātyāyana
893:by period
805:Minkowski
780:Kātyāyana
740:Descartes
685:Aryabhata
664:Geometers
648:Tesseract
512:Trapezoid
484:Rectangle
277:Dimension
162:Algebraic
152:Synthetic
123:Spherical
108:Euclidean
1990:Category
1966:See also
1766:Manifold
1608:See also
1335:denoted
1262:), with
1248:subspace
1200:1D space
1104:Poincaré
1048:Minggatu
1007:Yang Hui
977:Virasena
865:Yang Hui
860:Virasena
830:Poincaré
810:Minggatu
590:Cylinder
535:Diameter
494:Rhomboid
451:Altitude
442:Triangle
336:Symmetry
314:Parallel
299:Diagonal
269:Features
266:Concepts
157:Analytic
118:Elliptic
100:Branches
86:Timeline
45:Geometry
1888:Simplex
1826:Fractal
1685:(1961)
1270:(e.g.,
1246:, a 1D
1222:. Any
1214:, each
1202:) is a
1129:Coxeter
1109:Hilbert
1094:Riemann
1043:Huygens
1002:al-Tusi
992:Khayyám
982:Alhazen
949:1–1400s
850:al-Tusi
835:Riemann
785:Khayyám
770:Huygens
765:Hilbert
735:Coxeter
695:Alhazen
673:by name
610:Pyramid
489:Rhombus
433:Polygon
385:segment
233:Fractal
216:Digital
201:Complex
82:History
77:Outline
1845:shapes
1670:
1562:module
1523:is an
1475:sphere
1268:length
1236:circle
1150:Gromov
1145:Atiyah
1124:Veblen
1119:Cartan
1089:Bolyai
1058:Sakabe
1038:Pascal
931:Euclid
921:Manava
855:Veblen
840:Sakabe
815:Pascal
800:Manava
760:Gromov
745:Euclid
730:Cartan
720:Bolyai
710:Atiyah
620:Sphere
583:cuboid
571:Volume
526:Circle
479:Square
397:Length
319:Vertex
223:Convex
206:Finite
147:Affine
62:sphere
1949:Eight
1944:Seven
1924:Three
1801:Krull
1557:is a
1488:of a
1312:over
1283:field
1272:metre
1264:units
1242:. In
1228:curve
1216:point
1099:Klein
1079:Gauss
1053:Euler
987:Sijzi
957:Zhang
911:Ahmes
875:Zhang
845:Sijzi
790:Klein
755:Gauss
750:Euler
690:Ahmes
423:Plane
358:Point
294:Curve
289:Angle
66:plane
64:to a
1934:Five
1929:Four
1909:Zero
1843:and
1668:ISBN
1555:ring
1515:) =
1063:Aida
680:Aida
639:Four
578:Cube
545:Area
517:Kite
428:Area
380:Line
34:The
1939:Six
1919:Two
1914:One
1534:In
1277:In
1274:).
1266:of
1258:or
1254:" (
902:BCE
390:ray
2006::
1590:.
1550:.
1531:.
1503:⊂
1477:,
1194:A
60:a
1955:n
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1422:1
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1364:,
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