568:
238:
567:
81:
629:
563:
Lobachevsky discarded it. The full impact of the
Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry, for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
562:
The boldness of his challenge and its successful outcome have inspired mathematicians and scientists in general to challenge other "axioms" or accepted "truths", for example the "law" of causality which, for centuries, have seemed as necessary to straight thinking as Euclid's postulate appeared until
494:
Some mathematicians and historians have wrongly claimed that
Lobachevsky in his studies in non-Euclidean geometry was influenced by Gauss, which is untrue. Gauss himself appreciated Lobachevsky's published works highly, but they never had personal correspondence between them prior to the publication.
381:
of Kazan
University in 1827. In 1832, he married Varvara Alexeyevna Moiseyeva. They had a large number of children (eighteen according to his son's memoirs, though only seven apparently survived into adulthood). He was dismissed from the university in 1846, ostensibly due to his deteriorating health:
1399:
It was responsibility to supervise the students and to report their conduct to the principal. Kondyrev avenged himself by submitting very bad reports on
Lobachevsky, even to the extent of accusing him of atheism, a charge which was not at all justified but which might have had tragic consequences
650:
album. In the song, Lehrer portrays a
Russian mathematician who sings about how Lobachevsky influenced him: "And who made me a big success / and brought me wealth and fame? / Nikolai Ivanovich Lobachevsky is his name." Lobachevsky's secret to mathematical success is given as
1340:
His stubbornness, reported atheism, and genius supported his rise as a champion of the proletariat. To the
Soviets, Lobachevsky represented not just the greatness of the common man, emerging from a humble background as he did, he also was a revolutionary of
267:
495:
Although three people—Gauss, Lobachevsky and Bolyai—can be credited with discovery of hyperbolic geometry, Gauss never published his ideas, and
Lobachevsky was the first to present his views to the world mathematical community.
938:(1970) gives December 2, 1792. Further information on Lobachevsky's birthdate can be found in Papadopoulos (2010) However, note that page 207 incorrectly converts 1792-11-20 to 1792-12-02 instead of 1792-12-01
1359:
Though
Lobachevsky appears to have invented non-Euclidean geometry without the help of the Almighty, he built a church on the instructions of the University council. It is said that he was an atheist.
91:
1653:
1163:
by G. M. Polotovsky, PDF page 3: "Н.И.Лобачевский родился в Макарьевском уезде Нижегородской губернии в 1793 году" (quoting A. F. Popov (1857)); page 4: " местом рождения называет Макарьев".
713:), a forgotten colleague who is transferring to teach at another university, gives as the reason behind her departure that Columbia is the only holder of Nikolai Lobachevsky's manuscripts.
440:'s reformulation) that for any given line and point not on the line, there is only one line through the point not intersecting the given line. Lobachevsky would instead develop a
889:
613:
1693:
373:
and mathematics in 1811. In 1814 he became a lecturer at Kazan
University, in 1816 he was promoted to associate professor. In 1822, at the age of 30, he became a full
115:
456:) between 1829 and 1830. In 1829 Lobachevsky wrote a paper about his ideas called "A Concise Outline of the Foundations of Geometry" that was published by the
1136:
A. F. Popov, "Воспоминания о службе и трудах проф. Казанского университета Н. И. Лобачевского" ("Memoirs of the
Service and Work of N. I. Lobachevsky"), 1857
533:, named after two other mathematicians who discovered it independently. In Russia, it is called the Lobachevsky method. Lobachevsky gave the definition of a
338:
origin – Ivan Maksimovich Lobachevsky and Praskovia Alexandrovna Lobachevskaya. He was one of three children. When he was seven, his father, a clerk in a
448:), 1826 to the session of the department of physics and mathematics, and this research was printed in the periodical 'Kazan University Course Notes' as
812:
1683:
971:
1603:
1422:
854:
502:
was completed in 1823, but was not published in its exact original form until 1909, long after he had died. Lobachevsky was also the author of
1509:
1333:
1209:
491:
which has many applications. Hyperbolic geometry is frequently referred to as "Lobachevskian geometry" or "Bolyai–Lobachevskian geometry".
1622:
1688:
803:
1663:
934:
838:, translator and editor: A. Papadopoulos, Heritage of European Mathematics Series, Vol. 4, European Mathematical Society. 2010, 310 p.
1385:
1298:
475:
one line that can be extended through that point and run parallel to another line of which that point is not part. He developed the
1668:
358:
210:
538:
530:
1658:
1088:
920:
277:
273:
38:
894:
297:
31:
119:
1045:
1673:
1678:
1312:В 'шнуровой книге' университета сохранилась запись, что Лобачевский 'в значительной мере явил признаки безбожия'.
659:". According to Lehrer, the song is "not intended as a slur on character" and the name was chosen "solely for
1608:
1427:
1259:
1033:
996:
303:
479:
which depends on the distance the point is off the given line. In hyperbolic geometry the sum of angles in a
676:
1467:
1441:
869:
606:
534:
484:
421:
377:, teaching mathematics, physics, and astronomy. He served in many administrative positions and became the
351:
327:
289:
183:
125:
382:
by the early 1850s, he was nearly blind and unable to walk. He died in poverty in 1856 and was buried in
1161:"К 150-летию со дня смерти Н.И.Лобачевского" ("On the 150th anniversary of the death of N. Lobachevsky")
864:
705:
592:
488:
827:
1648:
1643:
1614:
1598:
1417:
1049:
879:
874:
696:
476:
362:
1127:
A. A. Andronov, "Где и когда родился Н.И.Лобачевский" ("Where and when was Lobachevsky born?"), 1956
1594:
1413:
1061:
Lobachevsky dictated two versions of that work, a first one in Russian, and a second one in French.
859:
646:
480:
468:
464:
403:
285:
919:
This is the date given by Kagan (1957) and Andronov (1956) (the latter gives 1 December [
709:, "Dick and the Single Girl" (season 2 episode 24) originally aired on May 11 1997, Sonja Umdahl (
460:
but was rejected when it was submitted to the St. Petersburg Academy of Sciences for publication.
1044:
Ivan Maksimovich Lobachevsky (Jan Łobaczewski in Polish) came from a Polish noble family of the
817:
710:
641:
554:
552:
wrote about Lobachevsky's influence on the following development of mathematics in his 1937 book
526:
522:
444:
in which the fifth postulate was not true. This idea was first reported on February 23 (Feb. 11,
293:
86:
237:
424:, also referred to as Lobachevskian geometry. Before him, mathematicians were trying to deduce
1505:
1462:
1381:
1329:
1294:
1205:
884:
849:
602:
598:
585:
378:
366:
153:
1539:
549:
394:
260:
220:
172:
1326:
The Fifth Postulate: How Unraveling a Two Thousand Year Old Mystery Unraveled the Universe
1255:
1185:
983:
429:
383:
347:
319:
1146:
1100:
781:
636:
A fictional mathematician named "Lobachevsky" is the subject of songwriter/mathematician
417:
1173:
1160:
323:
1637:
1380:(corrected reprint ed.). Princeton: Princeton University Press. pp. 56–57.
1008:
This is a quote from G. B. Halsted's translator's preface to his 1914 translation of
786:
691:
681:
667:
572:
518:
437:
335:
80:
17:
932:
Older sources in Russian—e.g., Popov (1857)—give 1793 rather than 1792, while the
628:
389:
In 1811, in his student days, Lobachevsky was accused by a vengeful supervisor of
1375:
1288:
1371:
1497:
1197:
1186:"Чье имя носит университет" ("After whose name the University has been named")
1021:
652:
637:
307:
42:
1261:
God Created the Integers: The Mathematical Breakthroughs that Changed History
1084:
445:
374:
339:
159:
1290:История и философия науки. Математика, вычислительная техника, информатика
791:
Non-Euclidean Geometry: A Critical and Historical Study of its Development
1565:"3rd Rock from the Sun, "Dick and the Single Girl" (season 2 episode 24)"
1052:
coats-of-arms, and was classified as a Pole in Russian official documents
1013:
674:
novella "Operation Changeling" – which was later expanded into the novel
660:
656:
441:
281:
200:
463:
The non-Euclidean geometry that Lobachevsky developed is referred to as
1025:
671:
390:
370:
50:
982:
Other sources in Russian—e.g., A. A. Andronov (1956)—give the city of
575:
coin commemorating the 200th anniversary of Lobachevsky's birth, 1992.
517:
Another of Lobachevsky's achievements was developing a method for the
416:
Lobachevsky's main achievement is the development (independently from
1439:
The 1914 English translation by George Bruce Halsted is available at
1029:
685:
425:
331:
1564:
1540:"Screen Rant, 10 Stars You Forgot Appeared On 3rd Rock From The Sun"
1174:
website of the Lobachevsky Nizhny Novgorod State University Museum
1017:
627:
436:. Euclid's fifth is a rule in Euclidean geometry which states (in
433:
350:
from 1802, graduating in 1807, and then received a scholarship to
343:
149:
1293:. Учебноее пособие. Saint Petersburg: БХВ-Петербург. p. 62.
541:
gave the same definition independently soon after Lobachevsky).
1374:(1982) . "Mathematical Reasoning from Eudoxus to Lobachevsky".
1470:. The University of Michigan Historical Mathematics Collection
1444:. The University of Michigan Historical Mathematics Collection
357:
At Kazan University, Lobachevsky was influenced by professor
310:
of Geometry" due to the revolutionary character of his work.
995:
Bell (1986) attributes this quote to another mathematician,
828:
New Principles of Geometry with Complete Theory of Parallels
742:
New Principles of Geometry with Complete Theory of Parallels
726:, Vol. I–IV (Russian), Moscow–Leningrad (GITTL), (1946–51).
280:
12 February] 1856) was a Russian mathematician and
354:, which had been founded just three years earlier in 1804.
318:
Nikolai Lobachevsky was born either in or near the city of
655:!", as long as one is always careful to "call it, please,
632:
Stamp of 1956 marking the centenary of Lobachevsky's death
588:, an asteroid discovered in 1972, was named in his honour.
361:, a former teacher and friend of the German mathematician
1628:
471:
with the statement that for any given point there exists
1623:
Nikolaj Ivanovič Lobačevskij - Œuvres complètes, tome 2
753:
Application of imaginary geometry to certain integrals
537:
as a correspondence between two sets of real numbers (
684:
with the assistance of the ghosts of Lobachevsky and
619:
A street in Ploiesti, Romania was named in his honor.
508:
Geometrical Investigations on the Theory of Parallels
823:. McGraw Hill 1929. Dover reprint, pp. 360–374.
1654:
19th-century mathematicians from the Russian Empire
342:office, died, and Nikolai moved with his mother to
276:
20 November] 1792 – 24 February [
230:
216:
206:
196:
179:
168:
134:
107:
62:
1118:, 1957 (first published in Russian in 1943), p. 26
30:"Lobachevsky" redirects here. For other uses, see
1151:, European Mathematical Society. 2010, pp. 206–7.
782:Geometrical Researches on the Theory of Parallels
731:Geometrical Researches on the Theory of Parallels
1629:Lobachevsky State University of Nizhny Novgorod
1116:N. Lobachevsky and His Contribution to Science
1105:, European Mathematical Society. 2010, p. 208.
816:. Excerpts translated by Henry P. Manning: in
986:rather than the Governorate as his birthplace
956:
250:
8:
1277:. Rocznik Wschodni. Issue 7–9. 2002. p. 163.
955:, at that time; nominative form in Russian:
724:N. I. Lobachevsky – Complete Collected Works
261:[nʲɪkɐˈlajɪˈvanəvʲɪtɕləbɐˈtɕefskʲɪj]
1377:The Nature and Growth of Modern Mathematics
1694:Academic staff of Kazan Federal University
1524:Liner notes, "The Tom Lehrer Collection",
1251:
1249:
1247:
1245:
1243:
789:(tr.). 1891. Reprinted in Roberto Bonola:
700:contains a poem dedicated to Lobachevsky.
79:
59:
1275:Mikołaj Łobaczewski - twórca pangeometrii
680:(1971) – a group of sorcerers navigate a
292:, and also for his fundamental study on
566:
1604:MacTutor History of Mathematics Archive
1423:MacTutor History of Mathematics Archive
1229:
1227:
1225:
1223:
1221:
1074:
912:
1328:. John Wiley & Sons. p. 186.
1235:A history of mathematics: Introduction
972:Makaryevsky uezd, Kostroma Governorate
1357:. Taylor & Francis. p. 329.
259:
7:
1264:. Running Press. 2007. pp. 697–703.
1080:
1078:
970:Not to be confused with Makaryev in
365:(1777-1855). Lobachevsky received a
334:) in 1792 to parents of Russian and
1148:Nikolai I. Lobachevsky. Pangeometry
1102:Nikolai I. Lobachevsky. Pangeometry
935:Dictionary of Scientific Biography
529:. This method is now known as the
284:, known primarily for his work on
25:
1538:Lennon, Madison (June 16, 2019).
1504:. Touchstone Books. p. 336.
1204:. Touchstone Books. p. 294.
408:'signs of godlessness').
27:Russian mathematician (1792-1856)
1684:Russian people of Polish descent
1615:Website dedicated to Lobachevsky
483:must be less than 180 degrees.
236:
1461:The 1902 German translation by
1287:Петров, Юрий Петрович (2012) .
1237:. Addison-Wesley. 2009. p. 842.
1172:Lobachevsky's biography at the
359:Johann Christian Martin Bartels
346:. Nikolai Lobachevsky attended
252:Никола́й Ива́нович Лобаче́вский
855:Gauss–Bolyai–Lobachevsky space
539:Peter Gustav Lejeune Dirichlet
487:stimulated the development of
1:
1145:Athanase Papadopoulos (ed.),
1099:Athanase Papadopoulos (ed.),
1089:Mathematics Genealogy Project
247:Nikolai Ivanovich Lobachevsky
97:
39:Eastern Slavic naming customs
923:20 November] 1792).
831:. G. B. Halsted (tr.). 1897.
821:A Source Book in Mathematics
298:Lobachevsky integral formula
32:Lobachevsky (disambiguation)
793:. 1912. Dover reprint 1955.
506:(1835–1838). He also wrote
504:New Foundations of Geometry
120:Nizhny Novgorod Governorate
1710:
1689:Burials at Arskoe Cemetery
1353:"The History of Science".
498:Lobachevsky's magnum opus
37:In this name that follows
36:
29:
1664:Mathematicians from Kazan
1184:Andrey Kalinin's article
957:
895:Poincaré half-plane model
735:On the Origin of Geometry
694:'s science fiction novel
450:On the Origin of Geometry
398:
251:
235:
226:
189:
78:
69:
1609:University of St Andrews
1428:University of St Andrews
1028:that was Lobachevsky to
997:William Kingdon Clifford
834:Nikolai I. Lobachevsky,
306:called Lobachevsky the "
304:William Kingdon Clifford
70:
1487:Papadopoulos 2010, p. v
1010:The Theory of Parallels
800:Lobachevski illuminated
764:Works on Other Subjects
616:was named in his honor.
595:was named in his honor.
467:. Lobachevsky replaced
272:; 1 December [
1669:Russian mathematicians
890:Lobachevsky University
870:Non-Euclidean geometry
682:non-Euclidean universe
633:
614:Lobachevsky University
607:Kazan State University
576:
565:
531:Dandelin–Gräffe method
485:Non-Euclidean geometry
422:non-Euclidean geometry
328:Nizhny Novgorod Oblast
290:Lobachevskian geometry
184:Lobachevskian geometry
156:, Russian Empire
126:Nizhny Novgorod Oblast
122:, Russian Empire
1599:"Nikolai Lobachevsky"
1418:"Nikolai Lobachevsky"
1324:Bardi, Jason (2008).
865:Hyperboloid structure
798:Also in: Seth Braver
706:3rd Rock from the Sun
631:
570:
560:
489:differential geometry
288:, otherwise known as
1659:Hyperbolic geometers
1595:Robertson, Edmund F.
1468:"Quod.lib.umich.edu"
1442:"Quod.lib.umich.edu"
1414:Robertson, Edmund F.
880:Lobachevsky function
875:Lobachevsky (crater)
773:English translations
697:Doorways in the Sand
477:angle of parallelism
363:Carl Friedrich Gauss
1593:O'Connor, John J.;
1412:O'Connor, John J.;
1085:Nikolai Lobachevsky
907:Informational notes
860:Hyperbolic geometry
722:Kagan V. F. (ed.):
647:Songs by Tom Lehrer
527:algebraic equations
481:hyperbolic triangle
465:hyperbolic geometry
454:О началах геометрии
294:Dirichlet integrals
286:hyperbolic geometry
72:Николай Лобачевский
64:Nikolai Lobachevsky
18:Nikolay Lobachevsky
1502:Men of Mathematics
1273:Jan Ciechanowicz.
1202:Men of Mathematics
749:Imaginary Geometry
711:Christine Baranski
640:'s humorous song "
634:
624:In popular culture
577:
555:Men of Mathematics
1674:Russian geometers
1511:978-0-671-62818-5
1463:Heinrich Liebmann
1335:978-0-470-46736-7
1233:Victor J. Katz.
1211:978-0-671-62818-5
885:Lobachevsky Medal
850:1858 Lobachevskij
603:mathematics award
599:Lobachevsky Prize
591:The lunar crater
586:1858 Lobachevskij
407:
399:признаки безбожия
367:Master of Science
244:
243:
207:Academic advisors
191:Scientific career
154:Kazan Governorate
116:Makaryevsky Uyezd
16:(Redirected from
1701:
1679:Russian atheists
1619:
1611:
1580:
1579:
1577:
1575:
1561:
1555:
1554:
1552:
1550:
1535:
1529:
1522:
1516:
1515:
1494:
1488:
1485:
1479:
1478:
1476:
1475:
1465:is available at
1459:
1453:
1452:
1450:
1449:
1437:
1431:
1430:
1409:
1403:
1402:
1400:for Lobachevsky.
1396:
1394:
1368:
1362:
1361:
1350:
1344:
1343:
1321:
1315:
1314:
1309:
1307:
1284:
1278:
1271:
1265:
1253:
1238:
1231:
1216:
1215:
1194:
1188:
1182:
1176:
1170:
1164:
1158:
1152:
1143:
1137:
1134:
1128:
1125:
1119:
1112:
1106:
1097:
1091:
1082:
1062:
1059:
1053:
1042:
1036:
1006:
1000:
993:
987:
980:
974:
968:
962:
960:
959:
945:
939:
930:
924:
917:
644:" from his 1953
469:Playfair's axiom
402:
400:
352:Kazan University
271:
270:
269:
263:
258:
254:
253:
240:
221:Nikolai Brashman
217:Notable students
211:J. C. M. Bartels
173:Kazan University
163:
145:
143:
138:24 February 1856
129:
124:(now Makaryevo,
102:
99:
95:
83:
73:
60:
21:
1709:
1708:
1704:
1703:
1702:
1700:
1699:
1698:
1634:
1633:
1617:
1592:
1589:
1584:
1583:
1573:
1571:
1563:
1562:
1558:
1548:
1546:
1537:
1536:
1532:
1523:
1519:
1512:
1496:
1495:
1491:
1486:
1482:
1473:
1471:
1466:
1460:
1456:
1447:
1445:
1440:
1438:
1434:
1411:
1410:
1406:
1392:
1390:
1388:
1372:Kramer, Edna E.
1370:
1369:
1365:
1352:
1351:
1347:
1336:
1323:
1322:
1318:
1305:
1303:
1301:
1286:
1285:
1281:
1272:
1268:
1256:Stephen Hawking
1254:
1241:
1232:
1219:
1212:
1196:
1195:
1191:
1183:
1179:
1171:
1167:
1159:
1155:
1144:
1140:
1135:
1131:
1126:
1122:
1113:
1109:
1098:
1094:
1083:
1076:
1066:
1065:
1060:
1056:
1043:
1039:
1007:
1003:
994:
990:
984:Nizhny Novgorod
981:
977:
969:
965:
946:
942:
931:
927:
918:
914:
904:
899:
845:
719:
677:Operation Chaos
626:
582:
547:
458:Kazan Messenger
430:fifth postulate
414:
384:Arskoe Cemetery
348:Kazan Gymnasium
320:Nizhny Novgorod
316:
296:, known as the
266:
265:
264:
256:
164:
157:
147:
141:
139:
130:
123:
112:
111:1 December 1792
103:
100:
89:
74:
71:
65:
58:
35:
28:
23:
22:
15:
12:
11:
5:
1707:
1705:
1697:
1696:
1691:
1686:
1681:
1676:
1671:
1666:
1661:
1656:
1651:
1646:
1636:
1635:
1632:
1631:
1626:
1625:– Gallica-Math
1620:
1612:
1588:
1587:External links
1585:
1582:
1581:
1556:
1530:
1517:
1510:
1489:
1480:
1454:
1432:
1404:
1386:
1363:
1355:Soviet Science
1345:
1334:
1316:
1299:
1279:
1266:
1239:
1217:
1210:
1189:
1177:
1165:
1153:
1138:
1129:
1120:
1107:
1092:
1073:
1072:
1064:
1063:
1054:
1037:
1034:W. K. Clifford
1001:
988:
975:
963:
940:
925:
911:
910:
903:
900:
898:
897:
892:
887:
882:
877:
872:
867:
862:
857:
852:
846:
844:
841:
840:
839:
832:
824:
808:
807:
795:
794:
777:
776:
774:
770:
769:
768:
767:
760:
745:
738:
718:
715:
703:In the sitcom
625:
622:
621:
620:
617:
610:
596:
589:
581:
578:
546:
543:
413:
410:
340:land-surveying
324:Russian Empire
315:
312:
249:(Russian:
242:
241:
233:
232:
228:
227:
224:
223:
218:
214:
213:
208:
204:
203:
198:
194:
193:
187:
186:
181:
180:Known for
177:
176:
170:
166:
165:
148:
146:(aged 63)
136:
132:
131:
113:
109:
105:
104:
84:
76:
75:
67:
66:
63:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1706:
1695:
1692:
1690:
1687:
1685:
1682:
1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1641:
1639:
1630:
1627:
1624:
1621:
1616:
1613:
1610:
1606:
1605:
1600:
1596:
1591:
1590:
1586:
1570:
1566:
1560:
1557:
1545:
1541:
1534:
1531:
1528:Factory, 2010
1527:
1521:
1518:
1513:
1507:
1503:
1499:
1493:
1490:
1484:
1481:
1469:
1464:
1458:
1455:
1443:
1436:
1433:
1429:
1425:
1424:
1419:
1415:
1408:
1405:
1401:
1389:
1387:9780691023724
1383:
1379:
1378:
1373:
1367:
1364:
1360:
1356:
1349:
1346:
1342:
1337:
1331:
1327:
1320:
1317:
1313:
1302:
1300:9785941576890
1296:
1292:
1291:
1283:
1280:
1276:
1270:
1267:
1263:
1262:
1257:
1252:
1250:
1248:
1246:
1244:
1240:
1236:
1230:
1228:
1226:
1224:
1222:
1218:
1213:
1207:
1203:
1199:
1193:
1190:
1187:
1181:
1178:
1175:
1169:
1166:
1162:
1157:
1154:
1150:
1149:
1142:
1139:
1133:
1130:
1124:
1121:
1117:
1114:V. F. Kagan,
1111:
1108:
1104:
1103:
1096:
1093:
1090:
1086:
1081:
1079:
1075:
1071:
1070:
1058:
1055:
1051:
1047:
1041:
1038:
1035:
1031:
1027:
1023:
1019:
1015:
1011:
1005:
1002:
998:
992:
989:
985:
979:
976:
973:
967:
964:
954:
950:
944:
941:
937:
936:
929:
926:
922:
916:
913:
909:
908:
901:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
866:
863:
861:
858:
856:
853:
851:
848:
847:
842:
837:
833:
830:
829:
825:
822:
819:
815:
814:
810:
809:
805:
801:
797:
796:
792:
788:
787:G. B. Halsted
784:
783:
779:
778:
775:
772:
771:
765:
761:
758:
754:
750:
746:
743:
739:
736:
732:
728:
727:
725:
721:
720:
716:
714:
712:
708:
707:
701:
699:
698:
693:
692:Roger Zelazny
689:
687:
683:
679:
678:
673:
669:
668:Poul Anderson
664:
662:
658:
654:
649:
648:
643:
639:
630:
623:
618:
615:
611:
608:
604:
600:
597:
594:
590:
587:
584:
583:
579:
574:
569:
564:
559:
557:
556:
551:
544:
542:
540:
536:
532:
528:
524:
520:
519:approximation
515:
513:
509:
505:
501:
496:
492:
490:
486:
482:
478:
474:
470:
466:
461:
459:
455:
451:
447:
443:
439:
438:John Playfair
435:
431:
427:
423:
419:
411:
409:
405:
396:
392:
387:
385:
380:
376:
372:
368:
364:
360:
355:
353:
349:
345:
341:
337:
333:
329:
325:
321:
313:
311:
309:
305:
301:
299:
295:
291:
287:
283:
279:
275:
268:
262:
248:
239:
234:
229:
225:
222:
219:
215:
212:
209:
205:
202:
199:
195:
192:
188:
185:
182:
178:
174:
171:
167:
161:
155:
151:
137:
133:
127:
121:
117:
110:
106:
93:
88:
82:
77:
68:
61:
56:
52:
49: and the
48:
44:
40:
33:
19:
1618:(in Spanish)
1602:
1574:February 26,
1572:. Retrieved
1568:
1559:
1549:February 27,
1547:. Retrieved
1543:
1533:
1525:
1520:
1501:
1492:
1483:
1472:. Retrieved
1457:
1446:. Retrieved
1435:
1421:
1407:
1398:
1391:. Retrieved
1376:
1366:
1358:
1354:
1348:
1339:
1325:
1319:
1311:
1304:. Retrieved
1289:
1282:
1274:
1269:
1260:
1234:
1201:
1192:
1180:
1168:
1156:
1147:
1141:
1132:
1123:
1115:
1110:
1101:
1095:
1068:
1067:
1057:
1040:
1009:
1004:
991:
978:
966:
952:
948:
943:
933:
928:
915:
906:
905:
835:
826:
820:
811:
799:
790:
780:
763:
756:
752:
748:
741:
734:
730:
723:
704:
702:
695:
690:
675:
665:
645:
635:
561:
553:
548:
516:
511:
507:
503:
499:
497:
493:
472:
462:
457:
453:
449:
418:János Bolyai
415:
388:
356:
317:
302:
246:
245:
190:
85:Portrait by
54:
46:
1649:1856 deaths
1644:1792 births
1544:Screen Rant
1498:Bell, E. T.
1198:Bell, E. T.
1046:Jastrzębiec
836:Pangeometry
818:D. E. Smith
813:Pangeometry
757:Pangeometry
642:Lobachevsky
593:Lobachevsky
512:Pangeometry
510:(1840) and
432:from other
175:(MSc, 1811)
101: 1839
90: [
87:Lev Kryukov
55:Lobachevsky
51:family name
1638:Categories
1474:2012-12-17
1448:2012-12-17
1022:Copernicus
902:References
747:Vol. III:
744:(1835–38).
737:(1829–30).
663:reasons".
653:Plagiarize
638:Tom Lehrer
550:E. T. Bell
500:Geometriya
308:Copernicus
142:1856-02-25
114:Makaryev,
43:patronymic
1393:18 August
1306:18 August
1069:Citations
953:Makaryevo
762:Vol. IV:
740:Vol. II:
473:more than
386:, Kazan.
375:professor
314:Biography
231:Signature
169:Education
162:, Russia)
160:Tatarstan
128:, Russia)
47:Ivanovich
1569:Imdb.com
1500:(1986).
1200:(1986).
1014:Vesalius
1012:: "What
958:Макарьев
949:Makaryev
947:spelled
843:See also
755:(1836);
751:(1835);
733:(1840);
729:Vol. I:
670:'s 1969
661:prosodic
657:research
573:1 rouble
571:Russian
535:function
514:(1855).
442:geometry
326:(now in
282:geometer
201:Geometry
1087:at the
1026:Ptolemy
1024:was to
1020:, what
1016:was to
759:(1856).
672:fantasy
605:by the
521:of the
420:) of a
406:
395:Russian
391:atheism
371:physics
322:in the
140: (
1526:Shout!
1508:
1384:
1341:sorts.
1332:
1297:
1208:
1030:Euclid
951:, not
686:Bolyai
580:Honors
545:Impact
434:axioms
426:Euclid
412:Career
379:rector
336:Polish
332:Russia
197:Fields
41:, the
1032:." —
1018:Galen
806:2011.
717:Works
523:roots
344:Kazan
158:(now
150:Kazan
94:]
1576:2024
1551:2024
1506:ISBN
1395:2022
1382:ISBN
1330:ISBN
1308:2022
1295:ISBN
1206:ISBN
1050:Łada
1048:and
921:O.S.
612:The
601:, a
446:O.S.
404:lit.
278:O.S.
274:O.S.
257:IPA:
135:Died
108:Born
804:MAA
666:In
525:of
428:'s
369:in
53:is
45:is
1640::
1607:,
1601:,
1597:,
1567:.
1542:.
1426:,
1420:,
1416:,
1397:.
1338:.
1310:.
1258:.
1242:^
1220:^
1077:^
802:,
785:.
688:.
558::
401:,
397::
330:,
300:.
255:,
152:,
118:,
98:c.
96:,
92:ru
1578:.
1553:.
1514:.
1477:.
1451:.
1214:.
999:.
961:.
766:.
651:"
609:.
452:(
393:(
144:)
57:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
