72:
47:
20:
299:
98:, he noticed that the dog ran along the beach for a certain distance before jumping into the water. Because the dog is faster on land, this technique minimizes the total retrieval time. He showed that the dog is able to calculate the optimal point to jump into the water, a problem Pennings must resort to
86:
psychology professor
Michael McBeath has proposed a simple model to explain how dogs play fetch. By mounting a camera on the head of a dog, he found that the dog changed its speed and direction in order to keep the frisbee's image in a constant position on its retina. This approach, called the linear
34:
game where an object, such as a stick or ball, is thrown a moderate distance away from the animal, and it is the animal's objective to grab and retrieve ("fetch") it. Many times, the owner of the animal will say "Fetch" to the animal before or after throwing the object. The game is usually played
105:
Perruchet and
Gallego have demonstrated a method for calculating this optimal path using calculus in a different way. They propose that the dog optimizes its behaviour on a moment-to-moment basis, choosing at each moment the path that allows it to maximize its speed of approach to the ball. This
50:
54:
53:
49:
48:
55:
52:
87:
optical trajectory, makes the frisbee appear to move in a linear path at a constant speed. McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls.
51:
106:
requires the dog to be able to accurately estimate its speed on both land and water, but does not rely on the premise that the dog plans the entire route in advance.
281:
240:
136:
319:
94:, has found that dogs are somehow able to calculate the optimal path to a ball thrown in the water. While playing Fetch with his
303:
83:
324:
204:
Pierre
Perruchet and Jorge Gallego (January 2006). "Do dogs know related rates rather than optimization?".
115:
221:
186:
273:
The Math
Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
277:
252:
213:
178:
148:
313:
91:
95:
71:
271:
163:
298:
19:
99:
270:
Keith Devlin (2005-03-10). "Elvis: the Welsh Corgi Who Knows
Calculus".
225:
190:
76:
217:
182:
70:
60:
45:
43:(especially kittens) have been known to engage in fetch behavior.
18:
40:
36:
31:
177:(3). Mathematical Association of America: 178–182.
212:(1). Mathematical Association of America: 16–18.
8:
90:Tim Pennings, a mathematics professor at
59:Playing fetch with a dog at the beach in
127:
7:
14:
297:
1:
239:Ivars Peterson (2006-02-18).
135:Ivars Peterson (2004-06-26).
206:College Mathematics Journal
171:College Mathematics Journal
341:
39:, but, in rare instances,
320:Dog training and behavior
276:. Thunder's Mouth Press.
162:Tim Pennings (May 2003).
164:"Do dogs know calculus?"
137:"Dogs Catching Frisbees"
80:
63:
24:
74:
58:
23:A dog catching a ball
22:
306:at Wikimedia Commons
147:(26). Archived from
116:Least Time Principle
67:Mathematics of fetch
251:(7). Archived from
245:Science News Online
141:Science News Online
241:"Calculating Dogs"
81:
64:
25:
302:Media related to
283:978-1-56025-672-4
56:
332:
301:
287:
257:
256:
236:
230:
229:
218:10.2307/27646266
201:
195:
194:
168:
159:
153:
152:
132:
57:
340:
339:
335:
334:
333:
331:
330:
329:
310:
309:
294:
284:
269:
266:
264:Further reading
261:
260:
238:
237:
233:
203:
202:
198:
183:10.2307/3595798
166:
161:
160:
156:
134:
133:
129:
124:
112:
79:fetches a stick
69:
46:
17:
12:
11:
5:
338:
336:
328:
327:
325:Throwing games
322:
312:
311:
308:
307:
293:
292:External links
290:
289:
288:
282:
265:
262:
259:
258:
255:on 2006-08-11.
231:
196:
154:
151:on 2006-06-14.
126:
125:
123:
120:
119:
118:
111:
108:
68:
65:
15:
13:
10:
9:
6:
4:
3:
2:
337:
326:
323:
321:
318:
317:
315:
305:
304:Dogs fetching
300:
296:
295:
291:
285:
279:
275:
274:
268:
267:
263:
254:
250:
246:
242:
235:
232:
227:
223:
219:
215:
211:
207:
200:
197:
192:
188:
184:
180:
176:
172:
165:
158:
155:
150:
146:
142:
138:
131:
128:
121:
117:
114:
113:
109:
107:
103:
101:
97:
93:
88:
85:
84:Arizona State
78:
73:
66:
62:
44:
42:
38:
33:
29:
21:
272:
253:the original
248:
244:
234:
209:
205:
199:
174:
170:
157:
149:the original
144:
140:
130:
104:
92:Hope College
89:
82:
27:
26:
96:Welsh Corgi
314:Categories
122:References
102:to solve.
16:Pet sport
226:27646266
110:See also
100:calculus
191:3595798
77:Spaniel
35:with a
280:
224:
189:
222:JSTOR
187:JSTOR
167:(PDF)
61:Japan
30:is a
28:Fetch
278:ISBN
41:cats
249:169
214:doi
179:doi
145:165
37:dog
32:pet
316::
247:.
243:.
220:.
210:37
208:.
185:.
175:34
173:.
169:.
143:.
139:.
75:A
286:.
228:.
216::
193:.
181::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
