What is this bike called?
My brother wants to know where he can get one as well.
http://montanaheritagecommission.com/Images/BigWheelBike.jpg

Good luck. Those have not been made since the 1800 is l believe. But you could probably have a frame built by a custom frame maker.

Penny-farthing

Dude, that'd be classic!! lol l might get one just to screw around on campus.

But l am pretty sure you can buy one off of someone is hands in craigslist (maybe)

These r called boneshakers or penny farthings. Essentially, just like a tricycle, the pedals r directly connected to the wheel. The speed & difficulty in pedaling the bike is directly dependent upon the size of the front wheel & how fast u can pedal.
For a history, follow the Wikipedia link.
It should be noted that it can be dangerous riding these. Use at ur own risk & preferably under supervision. Always wear a helmet when riding one of these.
You can see one of these in action below & there is a link for purchase of some bikes. You might also be able to get one from ur local bike shop on a special order. You might also want to look for one used.

The official name of that style of bike is an 'ordinary.' You can buy more modern versions, which have pneumatic tires, although l can not seem to find any links on the 'net right now. The new versions do not have such large front wheels & have a modern brake.

The style of bicycle we're most familiar with officially called a 'safety' bicycle, so named because having the rider sitting between two like-sized wheels minimized the problem of getting flipped over the handlebars when stopping or going down a steep hill. Ordinaries accounted for a lot of broken collarbones when they were the dominant style of bicycle.