I'm currently reading e: The Story of a Number, which it turns out is fascinating. Being a bit of a geek, I've amassed a respectable collection of books about numbers.
It all started with A History of Pi, which was great reading (with the exception of when the author goes off on tangents about the horrors of the Soviet Union (??). If you're nerdy, then you're aware of the usefulness and omnipresence of this number. If you've never really had much use for math, then it may surprise you that this number was once banned by the church and people have killed each other over it. It has quite a history, going back thousands of years, and the book is entertaining even for non-geeks. There's at least one other book solely about the number pi, though I haven't read it.
The next book I read whose subject was a single number was The Nothing that Is: A Natural History of Zero. Here is another number that has quite a long history. Perhaps surprisingly, it has a shorter history than pi despite being a number that is much more clearly understood by today's modern non-mathematician. Another good book, and no ranting about Soviets this time. And as before, there is another book on the subject which I haven't read.
For my birthday this year, I received two additional books about numbers. The first was The Golden Ratio: The Story of PHI, the World's Most Astonishing Number. This is a number about as old as pi, and at least as ubiquitous (and was also, at one time, banned by the church). I haven't read this book yet but it is near the top of my list. And, of course, there is a companion book which I haven't read.
And this brings me back to the book I'm reading now, all about e. This number stands out from the rest because it is relatively new, having been "invented" around the turn of the 18th century. e comes about naturally (sorry) from the development of logarithms, limits, and exponents—all of which were being formalized during the late 1600's. It is a number with astonishing properties, and for being as obscure as it is to people outside of science and finance, it is just bizzarely relevant. e also stands out as being a number with only a single book written about it. Most numbers have zero books, several bigshot numbers have two; e is one of the chosen few with but a single book.
Some other numbers with their own books: i, Γ, and ∞ [ok ok, not really a number... but equal to the sum of all numbers... so why not.]
And an honorable mention, which is actually not about a number at all but is math-related, makes a perfect number joke, and is probably among my top three favorite books of all time: The Dot and the Line: A Romance in Lower Mathematics.
I want to write a book about a number! But it seems that all of the really interesting ones are already spoken for. I once had a book called "The Encyclopedia of Wild and Fascinating Numbers" or some crap like that, and it tried to point out interesting triva about lots and lots of different numbers. Numbers like pi and e had pages and pages about them. Then there were the somewhat more obscure entries like:
9^9^9: The largest number that can be expressed with only three digits.
fascinating.


I think 666 would be a better number for your book.
Why the number 36? I bookmarked your blog a while back, as it seems we have similar interests (though you are much more active when it comes to sharing them online). Now I'm a bit spooked -- as 36 has been my favourite number for ages. Strange maybe, but it really evokes a strong feeling inside me. Disappointed to see no further mention of it in your post :)