Does anyone know what the Arabic numerals represent? Roman numerals are easy (e.g. III has 3 Is), and the origins of the Latin alphabet is also known (R= Hebrew Resh = rosh = “head”). But what is the connection between the Arabic numerals and the numbers they represent?
Yep, they originated in Egyptian hieroglyphics and progressed. Here is a good starting place for research:
http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/en.htm
The site you sent me was interesting, but I didn’t find the answer to my OP. In fact, I’m not sure what you wrote above is accurate, at least according to that site. They write that the Arabic symbols come from Hindu ones, but don’t mention Egypt as the source. They also don’t show pictures of the original Hindu numerals - perhaps a look at them would show the connection to the numbers.
Looking at Hindu numerals, it’s hard to see a big connection to all the numbers themselves. They seem to have already undergone developments that are hard to analyse at first glance.
“Our” numerals are more or less just a continuation of this system with stylistic changes ranging from slight to origin-obscuring.
My roommate has a poster on his wall with the various stages next to each other. He’s asleep right now, so I can’t tell you what it looks like, and I’m not about to try and find it on the web, but trust me, it’s cool and it answers your question perfectly. 
This got discussed in a thread a while back entitled American Indians vs Chinese
The discussion on this specific topic begins about 1/3 the way through the thread and has several links supporting the various arguments.