Hello.
I went to the zoo in Atlanta and while I was petting a goat, I realized it had rectangular pupils. Is there any reason for this? I’m extremely curious.
Tim
Really? I never noticed. I have to learn to look them in the eye when I talk to them. 
As I recall, they’re less rectangular and more like a frog’s pupils.
No idea why, though.
Mostly it’s because of a need to operate at low light levels. Humans are strictly diurnal and so only need to operate under fairly high light levels. The optimum pupil shape for this situation is a circle, since it allows an even spread of light over the most sensitive parts of the retina. However as light levels increase the pupil needs to increase in size to allow more light to fall on the retina.
Unfortunately there is a practical upper limit to how much a circular pupil can expand. The muscles that open the pupils have to pull on them from all sides, which means that the pupil has to contract all around. Producing large pupils in this manner requires a lot of stretching. A rectangular pupil in contrast can be opened in only one direction. The muscles can pull on only the long edge and produce a very large pupil in a manner analogous to pulling open curtains to create a large viewing field from a very small slit. Because muscles have absolute limits of contraction, circular pupils have absolute limits in size. If the muscles in a circular eye were large enough to create the same size pupil as a corresponding rectangular pupil, the muscles would no longer fit in the eyeball. The contraction rate would also be lower, decreasing the response of night vision.
Have a look at agoat at night time and the pupil will be almost circular, but huge.
Here’s an earlier thread.
http://boards.straightdope.com/sdmb/showthread.php?threadid=179445
This subject comes up quite a bit, and there are other threads in the archives should you care to look for them.
For the record, they look like this.
Do any other animals have rectangular pupils?
From many hours spent gazing lovingly into the eyes of a sheep, I can tell you that they also have rectangular pupils.
My parents are such goat pupils!