197:
234:
288:
31:
461:
186:
454:
447:
393:
471:
634:
385:
66:
225:, having traced such accounts as far back as the late 19th century, indicates that these anecdotes are unfounded.
215:, Bouguer defined a curve of pursuit to explore the way in which one ship might maneuver while pursuing another.
599:
608:
120:
546:
334:
253:
62:
or points representing pursuers and pursuees; the curve of pursuit is the curve traced by the pursuers.
536:
339:
307:
Typical drawings of curves of pursuit have each point acting as both pursuer and pursuee, inside a
324:
389:
311:, and having each pursuer pursue the adjacent point on the polygon. An example of this is the
218:
196:
364:
Mémoires de mathématique et de physique tirés des registres de l'Académie royale des sciences
241:
The path followed by a single pursuer, following a pursuee that moves at constant speed on a
584:
575:
362:(1732). "Sur de nouvelles courbes auxquelles on peut donner le nom de lignes de poursuite".
59:
629:
556:
522:
479:
439:
434:
287:
242:
233:
507:
359:
208:
200:
30:
623:
502:
377:
222:
312:
296:
412:
531:
17:
221:
has occasionally been credited with first exploring curves of pursuit. However
497:
246:
212:
565:
492:
329:
47:
589:
512:
487:
308:
70:
292:
27:
Class of curves traced by a point which follows another moving point
232:
195:
55:
29:
443:
382:
Chases and
Escapes: The Mathematics of Pursuits and Evasion
123:
598:
574:
555:
521:
478:
180:
165:
335:Circles of Apollonius#Apollonius pursuit problem
69:in time, the pursuee is always on the pursuer's
455:
8:
415:, with a slightly narrower definition that |
237:Curves of pursuit with different parameters
462:
448:
440:
65:With the paths of the pursuer and pursuee
122:
286:
351:
207:The pursuit curve was first studied by
203:'s 1732 article studying pursuit curves
7:
181:{\displaystyle L(t)=F(t)+xF'\!(t).}
58:constructed by analogy to having a
291:Curve of pursuit of vertices of a
95:, the pursued (leader), for every
25:
34:A simple pursuit curve in which
532:Pedal & Contrapedal curves
172:
166:
148:
142:
133:
127:
84:, the pursuer (follower), and
1:
470:Differential transforms of
651:
386:Princeton University Press
211:in 1732. In an article on
252:It is a solution of the
257:1 +
435:MacTutor Pursuit curve
304:
238:
204:
182:
43:
602:on a family of curves
559:defined by two points
290:
254:differential equation
236:
199:
183:
33:
537:Negative pedal curve
121:
38:is the pursuer and
578:defined by a point
525:defined by a point
388:. pp. 27–28.
366:(in French): 1–15.
325:Logarithmic spiral
305:
239:
205:
178:
44:
617:
616:
576:Binary operations
395:978-0-691-12514-5
283:Multiple pursuers
219:Leonardo da Vinci
73:. That is, given
16:(Redirected from
642:
557:Unary operations
523:Unary operations
480:Unary operations
464:
457:
450:
441:
400:
399:
374:
368:
367:
356:
278:
187:
185:
184:
179:
164:
113:
109:
98:
94:
83:
52:curve of pursuit
41:
37:
21:
18:Curve of pursuit
650:
649:
645:
644:
643:
641:
640:
639:
635:Pursuit–evasion
620:
619:
618:
613:
594:
570:
551:
517:
474:
468:
431:)| are constant
409:
404:
403:
396:
376:
375:
371:
360:Bouguer, Pierre
358:
357:
353:
348:
340:Pursuit–evasion
321:
285:
269: −
256:
231:
194:
157:
119:
118:
111:
100:
96:
85:
74:
39:
35:
28:
23:
22:
15:
12:
11:
5:
648:
646:
638:
637:
632:
622:
621:
615:
614:
612:
611:
605:
603:
596:
595:
593:
592:
587:
581:
579:
572:
571:
569:
568:
562:
560:
553:
552:
550:
549:
544:
539:
534:
528:
526:
519:
518:
516:
515:
510:
508:Parallel curve
505:
500:
495:
490:
484:
482:
476:
475:
469:
467:
466:
459:
452:
444:
438:
437:
432:
408:
407:External links
405:
402:
401:
394:
378:Nahin, Paul J.
369:
350:
349:
347:
344:
343:
342:
337:
332:
327:
320:
317:
284:
281:
230:
229:Single pursuer
227:
209:Pierre Bouguer
201:Pierre Bouguer
193:
190:
189:
188:
177:
174:
171:
168:
163:
160:
156:
153:
150:
147:
144:
141:
138:
135:
132:
129:
126:
42:is the pursuee
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
647:
636:
633:
631:
628:
627:
625:
610:
607:
606:
604:
601:
597:
591:
588:
586:
583:
582:
580:
577:
573:
567:
564:
563:
561:
558:
554:
548:
545:
543:
542:Pursuit curve
540:
538:
535:
533:
530:
529:
527:
524:
520:
514:
511:
509:
506:
504:
503:Inverse curve
501:
499:
496:
494:
491:
489:
486:
485:
483:
481:
477:
473:
465:
460:
458:
453:
451:
446:
445:
442:
436:
433:
430:
426:
422:
418:
414:
411:
410:
406:
397:
391:
387:
383:
379:
373:
370:
365:
361:
355:
352:
345:
341:
338:
336:
333:
331:
328:
326:
323:
322:
318:
316:
314:
310:
302:
298:
294:
289:
282:
280:
276:
272:
268:
264:
260:
255:
250:
248:
244:
235:
228:
226:
224:
223:Paul J. Nahin
220:
216:
214:
210:
202:
198:
191:
175:
169:
161:
158:
154:
151:
145:
139:
136:
130:
124:
117:
116:
115:
107:
103:
92:
88:
81:
77:
72:
68:
67:parameterized
63:
61:
57:
53:
49:
32:
19:
541:
472:plane curves
428:
424:
420:
416:
381:
372:
363:
354:
313:mice problem
306:
300:
297:mice problem
274:
270:
266:
262:
258:
251:
240:
217:
206:
110:there is an
105:
101:
90:
86:
79:
75:
64:
51:
45:
624:Categories
600:Operations
498:Dual curve
346:References
261: =
247:radiodrome
213:navigation
114:such that
566:Strophoid
413:Mathworld
265: (
609:Envelope
585:Roulette
493:Involute
427:′(
423:)| and |
419:′(
380:(2007).
330:Tractrix
319:See also
162:′
104: (
48:geometry
590:Cissoid
547:Caustic
513:Isoptic
488:Evolute
309:polygon
277:
245:, is a
192:History
71:tangent
630:Curves
392:
293:square
295:(the
108:) ≠ 0
99:with
60:point
56:curve
54:is a
390:ISBN
303:=4).
299:for
243:line
50:, a
275:y′′
249:.
46:In
626::
384:.
315:.
279:.
273:)
259:y′
102:F′
463:e
456:t
449:v
429:t
425:F
421:t
417:L
398:.
301:n
271:x
267:a
263:k
176:.
173:)
170:t
167:(
159:F
155:x
152:+
149:)
146:t
143:(
140:F
137:=
134:)
131:t
128:(
125:L
112:x
106:t
97:t
93:)
91:t
89:(
87:L
82:)
80:t
78:(
76:F
40:A
36:P
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
