231:
Zhao also described the structure of the universe as a flat Earth inside spherical heavens. He used the metaphor of a healthy and sick horse to describe the motions of the sun and moon. He labels the healthy horse as the sun and the unhealthy horse as the moon, and says that each starts at the same
227:
allowed for this to be proven. Zhao's method involved finding the perimeter of a 16384-sided polygon. A 2048-sided polygon would have sufficiently proved pi is near 355/113, however it is believed he was trying to prove that it was within Zu
Chongzhi’s interval, thus the need for 16384 sides. Zhao
251:
Zhao described an optical experiment he undertook in a chapter titled "Pinhole Image". In the experiment, he had two light sources - tables with candles on them - which he covered with a board with a hole in the center, and observed the light as it passed through the hole onto a screen above. In
228:
also claimed that the value of pi could never be exhaustively calculated. While the work is influential, it does not note all of the values to enough decimal places to get some of the results, and has been known to underestimate values (but says that there is some remainder).
252:
doing so, he found that a larger hole let more light through; more candles led to a brighter image; the shape of the image on the screen is independent of the shape and size of the pinhole; and that moving the screen further away led to a dimmer image.
232:
point and runs around a circle before noting how far the moon falls behind. This exercise found the moon to be slower than the sun. Additionally, it used a circular track, concerning
171:
after obtaining a secret book on alchemy from an immortal Daoist master. However, this commentary has been lost. The biography further claims that Zhao gave a manuscript of
484:
Volkov, Alexei 1996/97. The
Mathematical Work of Zhao Youqin: Remote Surveying and the Computation of π. Taiwanese Journal for Philosophy and History of Science 8: 129–189.
175:
to his disciple, Zhu Hui, while on his deathbed on Jiming mountain in the
Zhejiang Province. This manuscript was later published by Zhu's disciple, Zhang Jun. The
160:(Complete Perfection) School of Song-Yuan Daoism. He ordained the next patriarch, Chen Zhixu (who wrote the Daoist biography mentioned above), in 1329. The
215:"), where Zhao lists pairs of values of circumferences and diameters used to calculate pi in the past; he believed 355/113 to be the most accurate.
560:
122:
555:
167:
Song Lian's biography agrees that Zhao was a Daoist hermit, claiming that he spent either 10 or 20 years writing a commentary on the
236:, as opposed to considering a straight track. He also described an instrument used to calculate the angle between a star and the
117:
Zhao was born on July 26, 1271. Most information about Zhao comes from three, slightly conflicting, sources: a Daoist biography
518:
207:
methods, then finding the perimeter (circumference) of the shape (a circle, or close to it). The book contains a section, "
259:
dedicated to becoming immortal using meditation through "Inner
Alchemy." He also wrote at least two Daoist books,
224:
106:
164:
does not mention a date of death for him, suggesting he was alive when it was written between 1331 and 1335.
179:
states he died after 1368. This is not widely accepted as this would make him 97 at the time of death.
133:(宋濂). All biographies agree that Zhao was gifted in astronomy from a young age and that he was born in
343:
402:
464:
550:
545:
8:
503:
Encyclopaedia of the
History of Science, Technology, and Medicine in Non-Western Cultures
203:
by drawing a square and increasing the number of sides until it resembles a circle using
514:
365:
156:. Zhixu's biography says that Zhao was a Daoist hermit, and later a patriarch of the
510:
506:
433:
355:
233:
460:
498:
241:
157:
539:
369:
145:
78:
360:
153:
463:(2002). "Problems of pursuit: Recreational mathematics or astronomy?". In
434:"Zhao Youqin | Chinese astronomer, mathematician, and Daoist | Britannica"
220:
149:
237:
82:
469:
From China to Paris: 2000 Years of
Transmission of Mathematical Ideas
286:
Xian Fo tong yuan ( on the Common
Origins of Immortals and Buddhas)
261:
Xian Fo tong yuan ( on the Common
Origins of Immortals and Buddhas)
204:
130:
192:
216:
134:
86:
196:
125:, and two biographies in different editions of Zhao's own book
90:
144:
says that, as a child, he was injured during the war between
223:
had stated that pi was between 3.1415926 and 3.1415927, but
505:, Dordrecht: Springer Netherlands, pp. 1790–1792,
200:
265:
Jin dan nan wen (Difficult
Problems of Gold Cinnabar).
291:
Jin dan nan wen (Difficult
Problems of Gold Cinnabar)
213:
On Circumference and Diameter of the Symbol of Heaven
219:
had already discovered a method for finding pi, and
240:, and another used to find the differences in the
199:. He is most well-known for his method of finding
537:
359:
129:one written by Wang Wei and the other by
93:monk. He is most well known for his book
496:
182:
103:New Writing on the Image of Alteration,
538:
459:
344:"Zhao Youqin and His Calculation of π"
341:
99:New Elucidation of the Heavenly Bodies
337:
335:
333:
331:
329:
327:
497:Wang, Jinguang; Wang, Caiwu (2008),
492:
490:
480:
478:
455:
453:
428:
426:
424:
422:
397:
395:
393:
391:
389:
387:
385:
383:
381:
379:
325:
323:
321:
319:
317:
315:
313:
311:
309:
307:
561:13th-century Chinese mathematicians
119:Shangyangzi jindan dayao liexianzhi
58:Quanzhen School of Song-Yuan Daoism
13:
49:Jiming mountain, Zhejiang Province
14:
572:
487:
475:
471:. Steiner Verlag. pp. 62–63.
450:
419:
376:
304:
556:13th-century Chinese astronomers
511:10.1007/978-1-4020-4425-0_9191
342:Volkov, Alexeı̈ (1997-08-01).
255:Zhao has another extant book,
1:
297:
187:Zhao's most notable work is
112:
7:
501:, in Selin, Helaine (ed.),
105:wherein he described a new
77:(趙友欽 1271-?) was a Chinese
10:
577:
244:of two celestial objects.
403:"Zhao Youqin - Biography"
169:Book of Changes (Yi jing)
62:
54:
44:
25:
18:
269:
249:Ge xiang xin shu (革象新书),
189:Ge xiang xin shu (革象新书),
162:Shangyangzi jindan dayao
142:Shangyangzi jindan dayao
127:Ge xiang xin shu (革象新书),
95:Ge xiang xin shu (革象新书),
465:Dold-Samplonius, Yvonne
276:Ge xiang xin shu (革象新书)
361:10.1006/hmat.1997.2163
293:(no known extant copy)
191:in which he discussed
107:method to calculate pi
97:translated either as
348:Historia Mathematica
183:Discoveries/Theories
438:www.britannica.com
209:Qian xiang zhou bi
520:978-1-4020-4425-0
499:"Optics in China"
257:Xian Fo tongyuan,
234:angular distances
195:, astronomy, and
72:
71:
568:
530:
529:
528:
527:
494:
485:
482:
473:
472:
457:
448:
447:
445:
444:
430:
417:
416:
414:
413:
399:
374:
373:
363:
339:
281:Xian Fo tongyuan
173:Ge xiang xin shu
68:Ge xiang xin shu
65:
39:Jiangxi province
35:
33:
16:
15:
576:
575:
571:
570:
569:
567:
566:
565:
536:
535:
534:
533:
525:
523:
521:
495:
488:
483:
476:
458:
451:
442:
440:
432:
431:
420:
411:
409:
401:
400:
377:
340:
305:
300:
272:
242:right ascension
185:
177:Jiangxi tongzhi
115:
63:
50:
40:
37:
31:
29:
21:
12:
11:
5:
574:
564:
563:
558:
553:
548:
532:
531:
519:
486:
474:
461:Bréard, Andrea
449:
418:
375:
354:(3): 301–331.
302:
301:
299:
296:
295:
294:
288:
283:
278:
271:
268:
184:
181:
114:
111:
70:
69:
66:
60:
59:
56:
52:
51:
48:
46:
42:
41:
38:
27:
23:
22:
19:
9:
6:
4:
3:
2:
573:
562:
559:
557:
554:
552:
549:
547:
544:
543:
541:
522:
516:
512:
508:
504:
500:
493:
491:
481:
479:
470:
466:
462:
456:
454:
439:
435:
429:
427:
425:
423:
408:
404:
398:
396:
394:
392:
390:
388:
386:
384:
382:
380:
371:
367:
362:
357:
353:
349:
345:
338:
336:
334:
332:
330:
328:
326:
324:
322:
320:
318:
316:
314:
312:
310:
308:
303:
292:
289:
287:
284:
282:
279:
277:
274:
273:
267:
266:
262:
258:
253:
250:
245:
243:
239:
235:
229:
226:
225:Zhao's method
222:
218:
214:
210:
206:
202:
198:
194:
190:
180:
178:
174:
170:
165:
163:
159:
155:
151:
147:
143:
138:
136:
132:
128:
124:
120:
110:
108:
104:
100:
96:
92:
88:
84:
80:
79:mathematician
76:
67:
61:
57:
53:
47:
43:
36:July 26, 1271
28:
24:
17:
524:, retrieved
502:
468:
441:. Retrieved
437:
410:. Retrieved
406:
351:
347:
290:
285:
280:
275:
264:
260:
256:
254:
248:
246:
230:
212:
208:
188:
186:
176:
172:
168:
166:
161:
154:Song dynasty
141:
139:
126:
118:
116:
102:
98:
94:
74:
73:
64:Notable work
55:Organization
551:1335 deaths
546:1271 births
221:Zu Chongzhi
150:Kublai Khan
75:Zhao Youqin
20:Zhao Youqin
540:Categories
526:2022-06-30
443:2022-06-30
412:2022-06-30
298:References
238:North Pole
137:province.
123:Chen Zhixu
83:astronomer
32:1271-07-26
370:0315-0860
205:iterative
131:Song Lian
113:Biography
87:alchemist
407:MacTutor
193:geometry
158:Quanzhen
152:and the
467:(ed.).
217:Liu Hui
148:leader
135:Jiangxi
517:
368:
197:optics
146:Mongol
91:Taoist
89:, and
270:Works
515:ISBN
366:ISSN
263:and
211:" ("
140:The
45:Died
26:Born
507:doi
356:doi
247:In
121:by
101:or
542::
513:,
489:^
477:^
452:^
436:.
421:^
405:.
378:^
364:.
352:24
350:.
346:.
306:^
201:pi
109:.
85:,
81:,
509::
446:.
415:.
372:.
358::
34:)
30:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.