196:
63:; it is one of the handful of Hilbert's problems that remains wholly unresolved. Ragsdale formulated a conjecture that provided an upper bound on the number of topological circles of a certain type, along with the basis of evidence.
319:
In 1993, Ilia
Itenberg produced additional counterexamples to the Ragsdale conjecture, so Viro and Itenberg wrote a paper in 1996 discussing their work on disproving the conjecture using the "patchworking" technique.
287:
96:
39:
in her dissertation in 1906 and was disproved in 1979. It has been called "the oldest and most famous conjecture on the topology of real algebraic curves".
400:(1980). "Кривые степени 7, кривые степени 8 и гипотеза Рэгсдейл" [Curves of degree 7, curves of degree 8 and the hypothesis of Ragsdale].
491:
414:"Кривые степени 7, кривые степени 8 и гипотеза Рэгсдейл" [Curves of degree 7, curves of degree 8 and the hypothesis of Ragsdale].
450:
527:
484:
633:
47:
Ragsdale's dissertation, "On the
Arrangement of the Real Branches of Plane Algebraic Curves," was published by the
207:
48:
628:
477:
52:
602:
537:
402:
344:
Itenberg, Ilya; Oleg, Viro (1996). "Patchworking algebraic curves disproves the ragsdale conjecture".
582:
522:
292:
and showed that the inequality could not be further improved. This inequality was later proved by
191:{\displaystyle p\leq {\tfrac {3}{2}}k(k-1)+1\quad {\text{and}}\quad n\leq {\tfrac {3}{2}}k(k-1).}
597:
557:
552:
512:
607:
60:
592:
460:
427:
371:
8:
567:
572:
587:
562:
517:
375:
312:
introduced a technique known as "patchworking algebraic curves" and used to generate a
305:
547:
446:
36:
532:
456:
423:
353:
32:
28:
75:
542:
313:
293:
622:
56:
445:. Oberwolfach Seminars. Vol. 35. Basel: Birkhäuser. pp. 34–35.
21:
469:
501:
357:
24:
397:
309:
304:
The conjecture was held of very high importance in the field of real
441:
Itenberg, Ilia; Mikhalkin, Grigory; Shustin, Eugenii (2007).
323:
The problem of finding a sharp upper bound remains unsolved.
370:
440:
376:"Biographies of Women in Mathematics: Virginia Ragsdale"
156:
107:
210:
99:
308:for most of the twentieth century. Later, in 1980,
281:
190:
620:
42:
27:that concerns the possible arrangements of real
61:22 other unsolved problems of the 19th century
485:
51:in 1906. The dissertation was a treatment of
343:
299:
339:
337:
335:
282:{\displaystyle |2(p-n)-1|\leq 3k^{2}-3k+1,}
492:
478:
71:Ragsdale's main conjecture is as follows.
499:
332:
621:
364:
473:
90:odd ovals. Ragsdale conjectured that
396:
13:
14:
645:
148:
142:
49:American Journal of Mathematics
434:
390:
346:The Mathematical Intelligencer
241:
231:
219:
212:
201:She also posed the inequality
182:
170:
133:
121:
1:
352:(4). Springer-Verlag: 19–28.
326:
66:
55:, which had been proposed by
43:Formulation of the conjecture
416:Soviet Mathematics - Doklady
7:
443:Tropical algebraic geometry
53:Hilbert's sixteenth problem
10:
650:
403:Doklady Akademii Nauk SSSR
508:
300:Disproving the conjecture
374:; Wicklin, Frederick J.
634:Real algebraic geometry
283:
192:
629:Disproved conjectures
528:Euler's sum of powers
378:. Anges Scott College
284:
193:
35:. It was proposed by
208:
97:
59:in 1900, along with
316:to the conjecture.
18:Ragsdale conjecture
518:Chinese hypothesis
358:10.1007/BF03026748
306:algebraic geometry
279:
188:
165:
116:
616:
615:
452:978-3-7643-8309-1
422:: 566–570. 1980.
164:
146:
115:
37:Virginia Ragsdale
641:
568:Ono's inequality
494:
487:
480:
471:
470:
465:
464:
438:
432:
431:
411:
394:
388:
387:
385:
383:
368:
362:
361:
341:
288:
286:
285:
280:
260:
259:
244:
215:
197:
195:
194:
189:
166:
157:
147:
144:
117:
108:
33:projective plane
31:embedded in the
29:algebraic curves
649:
648:
644:
643:
642:
640:
639:
638:
619:
618:
617:
612:
504:
498:
468:
453:
439:
435:
413:
410:(6): 1306–1309.
395:
391:
381:
379:
372:De Loera, Jesús
369:
365:
342:
333:
329:
302:
255:
251:
240:
211:
209:
206:
205:
155:
143:
106:
98:
95:
94:
76:algebraic curve
74:Assume that an
69:
45:
12:
11:
5:
647:
637:
636:
631:
614:
613:
611:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
543:Hauptvermutung
540:
535:
530:
525:
520:
515:
509:
506:
505:
497:
496:
489:
482:
474:
467:
466:
451:
433:
412:Translated in
398:Viro, Oleg Ya.
389:
363:
330:
328:
325:
314:counterexample
301:
298:
290:
289:
278:
275:
272:
269:
266:
263:
258:
254:
250:
247:
243:
239:
236:
233:
230:
227:
224:
221:
218:
214:
199:
198:
187:
184:
181:
178:
175:
172:
169:
163:
160:
154:
151:
141:
138:
135:
132:
129:
126:
123:
120:
114:
111:
105:
102:
68:
65:
44:
41:
9:
6:
4:
3:
2:
646:
635:
632:
630:
627:
626:
624:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
510:
507:
503:
495:
490:
488:
483:
481:
476:
475:
472:
462:
458:
454:
448:
444:
437:
429:
425:
421:
417:
409:
405:
404:
399:
393:
377:
373:
367:
359:
355:
351:
347:
340:
338:
336:
331:
324:
321:
317:
315:
311:
307:
297:
295:
276:
273:
270:
267:
264:
261:
256:
252:
248:
245:
237:
234:
228:
225:
222:
216:
204:
203:
202:
185:
179:
176:
173:
167:
161:
158:
152:
149:
139:
136:
130:
127:
124:
118:
112:
109:
103:
100:
93:
92:
91:
89:
85:
81:
77:
72:
64:
62:
58:
54:
50:
40:
38:
34:
30:
26:
23:
19:
577:
538:Hedetniemi's
442:
436:
419:
415:
407:
401:
392:
380:. Retrieved
366:
349:
345:
322:
318:
303:
291:
200:
87:
83:
79:
73:
70:
46:
22:mathematical
17:
15:
598:Von Neumann
502:conjectures
78:of degree 2
623:Categories
608:Williamson
603:Weyl–Berry
583:Schoen–Yau
500:Disproved
461:1162.14300
428:0422.14032
327:References
67:Conjecture
25:conjecture
310:Oleg Viro
294:Petrovsky
262:−
246:≤
235:−
226:−
177:−
153:≤
128:−
104:≤
86:even and
82:contains
578:Ragsdale
558:Keller's
553:Kalman's
513:Borsuk's
382:22 March
588:Seifert
563:Mertens
57:Hilbert
593:Tait's
548:Hirsch
523:Connes
459:
449:
426:
573:Pólya
533:Ganea
20:is a
447:ISBN
384:2019
16:The
457:Zbl
424:Zbl
408:254
354:doi
145:and
625::
455:.
420:22
418:.
406:.
350:18
348:.
334:^
296:.
493:e
486:t
479:v
463:.
430:.
386:.
360:.
356::
277:,
274:1
271:+
268:k
265:3
257:2
253:k
249:3
242:|
238:1
232:)
229:n
223:p
220:(
217:2
213:|
186:.
183:)
180:1
174:k
171:(
168:k
162:2
159:3
150:n
140:1
137:+
134:)
131:1
125:k
122:(
119:k
113:2
110:3
101:p
88:n
84:p
80:k
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.