FWIW, Oregon is the only state with a flag that has two different sides. The front side has the state seal in yellow (or gold) on a field of blue; the reverse is a beaver (also in yellow on blue).
OK, you were going to say it… first time you ever saw a beaver on the back side.
But it’s true about the flag.
I guess the possibility exists that somewhere there’s a staff photographer for The Beaver Sentinel.
You left out the second half: “… while the MIT student is the animal of the engineer kingdom”.
The sports teams are club-quality, but MIT did have the national champion tiddlywinks team once.
Anyone who wants to try can come up with appropriate puns for when the USC Trojans play the Oregon State Beavers.
I encountered this term twice when I was attending Redondo Union High School in Redondo Beach, CA, 1964-67.
The first time was ibn a funny skit at a midday pep rally during the 1965 football season. Some of the big guys from the team came in wearing garish wigs and ridiculous dresses, and sat down on a bench on one side of the gym. Apparently at least one of them sat with his legs too far apart; as a friend later told me, some guy across the floor hollered to them, “Thanks for the beaver shot!” I asked, “What’s a ‘beaver shot’?” The friend said, “That’s when you get a look up a girl’s dress.”
The second time happened about a year later. A girl seated to my right in English class had the word “BEAVER SHOT” written as one of her personal graffiti on her notebook. I wasn’t close to this girl and I found out many years later she died young. 
You may also care to read Ball Four by Jim Bouton…
There is a town in Utah called Beaver.
Going south on I-15, just before Beaver, there is a town called Filmore.
A few years ago I was at ECTS, the European videogame trade show.
One of the distributors was pushing a children’s game called, I kid you not, Stinky & Beaver’s Wood Olympics.
Here’s the website:
Apparently someone tipped them off and they changed the name to Stinky & Stomper for the U.S. release, but if you look closely at the little picture of the sell sheet on the web page you can still make out “Stinky Beaver”.
and
Around these parts (Central Texas), this is also called a squirrel shot. I guess any fairly rodent-like mammal will work.
Don’t forget about Detroit’s Big Beaver Road, which is approriately reached via exit 69.