I don't know very much about rocks, but I looked through our rock identification books trying to match it to the pictures. I also tried looking online, and found lots of rock and mineral identification websites, but couldn't find anything that looked exactly like it.
It turns out, rock identification is more more involved than I would have thought. With plants, birds, trees, etc., a good field guide is enough. But with rocks, you need to determine the hardness, the composition, the luster, the cleavage, and more, and still an ID is not certain.
Since I was striking out, I did the only thing I could think of: ask someone smarter than me. I sent the photos I had to friends of mine who work as naturalists, and I posted the photos on PicAnswers.com.
PicAnswers.com is a question-and-answer website, but instead of just posting a question, you post a photograph of something you need identified. I had never used it before, but posting this this mystery rock was a perfect opportunity to try it out.
Only one person responded, but he identified it as Calcite, which is what my naturalists friends thought it was, too. Having the same answer coming from multiple sources is good, but when I looked up Calcite in our books and online, it doesn't really look like the rock my brother found - which shows why actually knowing what you're talking about is important.