• Fetch 5 8 Ball Bearings
• Fetch 5 8 Ball Miniclip
• Fetch 5 8 Ball Balls

Fetch is a pet 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 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 with a dog, but in rare instances cats, especially younger cats, have been known to engage in fetch behavior.

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Mathematics of Fetch[edit]

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Arizona State 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 Optical Trajectory, makes the frisbee appear to move in a linear path at a constant speed. Annotation edit 1 9 82 download free. McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls.^[1]

Tim Pennings,^[2] a mathematics professor at Hope College, has found that dogs are somehow able to calculate the optimal path to a ball thrown in the water. While playing Fetch with his Welsh Corgi, 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 with statistical significance, a problem Pennings must resort to calculus to solve.

Perruchet and Gallego^[3] 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 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.^[4]

See also[edit]

References[edit]

1. ^Ivars Peterson (2004-06-26). 'Dogs Catching Frisbees'. Science News Online. 165 (26). Archived from the original on 2006-06-14.
2. ^Tim Pennings (May 2003). 'Do dogs know calculus?'(PDF). College Mathematics Journal. Mathematical Association of America. 34 (3): 178–182. doi:10.2307/3595798. JSTOR3595798.
3. ^Pierre Perruchet and Jorge Gallego (January 2006). 'Do dogs know related rates rather than optimization?'. College Mathematics Journal. Mathematical Association of America. 37 (1): 16–18. doi:10.2307/27646266. JSTOR27646266.
4. ^Ivars Peterson (2006-02-18). 'Calculating Dogs'. Science News Online. 169 (7). Archived from the original on 2006-08-11.

Further reading[edit]

• Keith Devlin (2005-03-10). 'Elvis: the Welsh Corgi Who Knows Calculus'. The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). Thunder's Mouth Press. ISBN978-1-56025-672-4.

External links[edit]

• Media related to Dogs fetching at Wikimedia Commons

Fetch can be a very rewarding game to play with your dog. It engages both mind and body and can be used as reinforcement for other behavior. You sit for me and I’ll send this tennis ball flying through the air so you can chase after it.

Fetch by the Rules

Most of the time, when I play fetch I have the following two ground rules:

• Please plant your paws on the ground. I like my legs without scratches thank you.
• Please drop the ball so I can pick it up or put it in my hand and release it.

If one of the ground rules are broken, play ends (not forever, but for at least a little while).

Enter 2 Ball Fetch

Fetch 5 8 Ball Bearings

2 Ball Fetch is a great way to help teach the rules of the game.

Adobe xd reader. Materials needed:

• A Dog
• 2 Balls (sometimes the ones with squeaker help encourage dropping)
• Clicker (optional – you can just say “yes” the minute the ball is dropped)
• A couple of treats

Fetch 5 8 Ball Miniclip

Instructions:

• Ask your dog to sit, lay down, or do some other behavior he knows well.
• Toss the ball the minute he does the behavior.
• As he returns, as long as feet stay on the ground, show the second ball (if it has a squeaker you can do that too).
• As soon as his mouth opens to drop the ball, click, and throw the other ball.
• Pick up the dropped ball as he is running off.
• After several repetitions, he will start dropping the ball as he approaches.

Tip #1: Remember, if his feet come up, simply walk away and end play. You don’t have to say anything and no need to be upset. Ending play is enough of a consequence that after a few times he won’t be doing that again.

Fetch 5 8 Ball Balls

Tip #2: Some dogs will run around a few minutes with the ball, ignore the behavior and wait for the drop, click and reinforce. It won’t take long before they get bored with playing all by themselves.