Fetch is a

pet A pet, or companion animal, is an animal kept primarily for a person's company or entertainment rather than as a working animal, livestock, or a laboratory animal. Popular pets are often considered to have attractive appearances, intelligence ...

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 with a dog, but in rare instances

cat The cat (''Felis catus'') is a domestic species of small carnivorous mammal. It is the only domesticated species in the family Felidae and is commonly referred to as the domestic cat or house cat to distinguish it from the wild members of ...

s, especially younger cats, have been known to engage in fetch behavior.

Mathematics of Fetch

Arizona State Arizona State University (Arizona State or ASU) is a public research university in the Phoenix metropolitan area. Founded in 1885 by the 13th Arizona Territorial Legislature, ASU is one of the largest public universities by enrollment in the ...

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. McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls. Tim Pennings, a mathematics professor at

Hope College Hope College is a private Christian liberal arts college in Holland, Michigan. It was originally opened in 1851 as the Pioneer School by Dutch immigrants four years after the community was first settled. The first freshman college class matricu ...

, 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 The Welsh Corgi ( or Corgi, plural Corgis, or occasionally the etymologically consistent Corgwn; ) is a small type of herding dog that originated in Wales. The name ''corgi'' is derived from the Welsh words and (which is mutated to ), me ...

, 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

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

to solve. 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 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.

References

External links

* {{DEFAULTSORT:Fetch (Game) Dog training and behavior Throwing games

Mathematics of Fetch

See also

References

Further reading

External links