There are many ways that math shows up in the world around us. For example, take a look at this:
I know, I know. Just from that sentence and picture you're thinking to yourself "Jess? Is that you? YOU DON'T MATH! WHO HAS YOU KIDNAPPED?!?" lol. And the best part is, that isn't even the entire equation! Here's the tail end:
Now to you folks who actually know math and stuff, this probably doesn't look like much. But when one of my professors earlier this summer put this on the board during a lecture I was like "I'm done for!" Surprisingly, this formula was actually pretty easy to understand once it was explained.
These mysterious equations are what is known in the library cataloging/bibliography world as a collational formula. Perhaps you are familiar with the term "collate" or "collated" when it comes to printing? The collational formula is a set way for bibliographers or catalogers to describe a book's physical contents in terms of # of pages, # of "signatures" or groups of pages, and some other factors. Let me break it down for ya'll.
Part 1: The beginning.
The "pi" symbol is used in place of what are called "unsigned leaves." Maybe you have opened a book before and seen blank pages at the beginning? Pi and the number "attached" to it indicate the number of "unsigned" leaves (or pages) at the beginning of the book. It is important to note that there could be things written on the pages; what is meant by "unsigned" is that most old, hand printed books had letters and numbers at the bottom of the pages so that printers and bookbinders would know what order the pages went in. But, since title pages, table of contents, etc. sometimes say the number of pages or page number where something appears in the book, they had to be printed LAST not first, which is why they were unsigned. I hope that made sense. Then the small letters a-c indicates pages/signatures that have been signed with these lowercase letters; again, these pages are likely a table of contents, list of illustrations, preface, forward, author's note, etc. etc.
Part 2: The text itself!
The A-K and K-U and U-Z indicate something interesting to note about hand printed books. As I mentioned before, printers had to have a way to indicate the order in which the signatures, or tiny groups of pages, would be stacked and then sewn together by bookbinders. They used the alphabet, "numbering" the bottoms of pages beginning with the capital letter A1 (usually; every printer had their own system, though). Then you will see A2, A3, A4, etc., usually until the fold or middle of the signature. Think of a signature like this: imagine a small stack of regular old computer paper, let's say 3 pages. If you folded that small stack in half you would then be able to "number" the pages A1, A2, etc., but ONLY on the FRONT of each page. So the "cover" of your tiny pamphlet would be A1, then the next page (NOT the reverse side) is A2, etc.
Wow this is kind of confusing to type out.
But anyway, the numbers after the letters indicate how many pages are in each signature, and the letters "J" and either "U" or "V" are always skipped because those letters didn't used to exist in the old English alphabet!
Part 3: the additional signatures
You may be thinking to yourself, "but what about long books with more than 24 signatures? how did they get to the end of the alphabet then keep going?" Additional signatures and their pages were noted by Aa, or AA, or aa, or whatever new combo the printer came up with (again, each one was different).
Part 4: The final notes!!
These notes tell us a little more about the book. For example, the (*4) indicates that there are 4 "signed" leaves in each signature. So, if we were looking at the book, in the first signature (again, a group of pages) we would see A1, then A2, then A3, then A4, and then nothing on the next few pages until we got to B1. The plus/minus "C" part indicates a cancel. A cancel is when somebody messed up while printing, or there was offensive material, or some unforseen problem with the text, so they would have to go through each and every page with the "cancellandum" or "error" and take it out, and replace it with a "cancellans" or "correction." It could be a letter, a paragraph, or even an entire page. The letter "C" indicates that the cancellans in this book was on the 6th leaf of the "C" signature.
So that is it!! Library math! It's not EXACTLY math, but to me it seems like math, so that's what I'm going to call it. Thanks for bearing with me if you've read this far......I think it's really interesting but I'm sure I'm the only one, lol! Bibliographers and catalogers use this formula to keep careful records of the structure of their books, especially if someone has to take them apart for repairs, digital scanning, etc. It makes it much easier when you're putting it back together to have a thorough formula to work from!