Theory and Applications of Continued Fractions MATH X 451.50 | Fall 2022

Theory and Applications of Continued Fractions MATH X 451.50 | Fall 2022
For the Fall 2022 offering Dr. Michael Miller is offering a mathematics course on Theory and Applications of Continued Fractions at UCLA on Tuesday nights through December 6th. We started the first class last night, but there have been issues with the course listing on UCLA Extension, so I thought I’d post here for any who may have missed it. (If you have issues registering, which some have, call the Extension office to register via phone.)

For almost 300 years, continued fractions—that is, numbers representable as the sum of an integer and a fraction whose denominator is itself such a sum—have fascinated mathematicians with both their remarkable properties and their myriad applications in such fields as number theory, differential equations, and computer algorithms. They have been applied to piano tuning, baseball batting averages, rational tangles, paper folding, and plant growth … the list goes on. This course is a rigorous introduction to the theory and mathematical applications of continued fractions. Topics to be discussed include quadratic irrationals, approximation of real numbers, Liouville’s Theorem, linear recurrence relations and Pell’s equation, Hurwitz’ Theorem, measure theory, and Ramanujan identities.

Mike is recommending the Continued Fractions text by Aleksandr Yakovlevich Khinchin. I found a downloadable digital copy of the 1964 edition (which should be ostensibly the same as the current Dover edition and all the other English editions) at the Internet Archive at  Based on my notes, it looks like he’s following the Khinchin presentation fairly closely so far.

If you’re interested, do join us on Tuesday nights this fall. (We’ve already discovered that going 11 for 37 is the smallest number of at bats that will produce a 0.297 batting average.) 

If you’re considering it and are completely new, I’ve previously written up some pointers on how Dr. Miller’s classes proceed: Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

This post was originally published on Chris Aldrich

Brodart Library Supplies for the Analog Zettelkasten Enthusiast

So you’ve taken the plunge and purchased an old school library card catalog, or maybe you want to but haven’t hit critical mass of cards to justify the purchase yet? Certainly you’ve found the traditional index card supplies still available at every office supply store on the planet, but did you know there’s still at least one company that supports libraries with custom card catalog supplies that you could use with your zettelkasten?

Brodart is a library services company based in Pennsylvania that supplies materials to institutional libraries that still has a variety of supplies not only for libraries and book lovers alike, but for amateur and professional zettelmacher(in) as well.

Most of their focus is on 3-by-5 inch index card sized material, but maybe with the re-popularization, they might add more support for the 4-by-6 inch card enthusiasts?

Perhaps if the demand for these older systems goes up, they’ll not only have more offerings, but the price will come down through economies of scale?

Let’s look at what they’ve got available.

Cards and Card Guides

On the card side, they’ve got a variety of options that aren’t as readily available at most office supply stores. If you’ve got an old school library card catalog with rods, you’re probably going to want cards with holes pre-punched. Of course they’ve got them in colors as well as without holes too.

With a sizeable card collection you’re likely to want some card guides, so they offer the traditional A-Z 1/5 Cut Card Guides as well as Blank Catalog Card Guides, with those holes pre-punched for convenience.

3x5" 1/3 cut manilla card guides with pre cut holes for separating your card sections

Dewey Decimal Catalog Card Guides

Most may already have an indexing system built into their system, but if you don’t and want to go with a classic Dewey Decimal set up, they’ve got you covered.

Dewey Decimal system manilla card with a tab that reads "000 General Works". The card has the BroDart logo and the number 24-111-101.

Perhaps you’ve got a sizeable digital card collection already, and have been jonesing to make the jump to analog? They’ve got printable card sheets so you can print out your digital cards relatively easily and continue without losing all that work. Or maybe you’re the mid century/ Umberto Eco purist who wants typewritten cards, but don’t want to retype them all? They’ve got both 4-up and 3-up versions as well.

A perforated sheet of paper with outlines for 4 3x5" cards with pre-drilled holes in each.
4-Up Catalog Card Sheets for Laser Printers

Let’s say you’ve got a long standing practice of making bibliographic cards. You need some cards to hold not only your meta data about the materials you’re reading, but you want to add your fleeting notes to them the way Luhmann and others have. Brodart has a wide variety of pre-printed cards that could serve this purpose. Some have printed sections which say “Date Loaned” and “Borrowers’s Name”, with sections for data below, but these could just as easily stand for page number and lined space for your important notes.

Brodart White Book Cards with Author, Title, Date Loaned, and Borrower’s Name

A 5x3" card that would appear in a library book with an empty section at the top followed by fields labeled "Author" and "Title". Below these are a two colum set of lined spaces under headings for "Date Loaned" and "Borrower's Name".

There are also a number of other versions of this sort of card depending on what you want. Try these or search for the many others which may suit your fancy:

Slip Boxes

Maybe you haven’t made that slip box purchase yet, but want something shiny and new? Brodart has you covered here as well. They’ve got a few different options for a small desktop slip box or a fully modular system that you can add to over time.

Stand alone boxes

Brodart has at least two desktop boxes, with 12 and 9 drawers respectively.

A wooden table top library card catalog with drawers in a 4x3 configuration. Each drawer has a metal pull with a label slot and at the bottom a removable card file rod.

Modular Boxes

Want to design your own system that’s expandable with your card collection? They’ve got a five drawer wide system with options for 1, 2, or 3 row tall sections that you can build up to suit your needs. Start with their table and legs, add a one or more sections of card files, and then top it off with a cover. If you’d like, they’ve also got an interstitial piece with drawer pulls so that you’ve got a writing surface built into your zettelkasten. Build that system up to your ceiling!

A modular 3x5 drawer card catalog box. The top is open so as to accomodate other similar modular boxes or a woodenn cap top.

4-by-6 inch Card Boxes

Brodart is a bit thin on the 4-by-6 inch category, but for the beginning zettelmacher(in), they do have some nice sized, portable, archive quality boxes you might like to start your collection. See their Postcard Boxes.

Other Options

Of course there are lots of other options in the space. Some of these box systems can become pretty expensive, and for the price you might be as well off purchasing a used card catalog which you can restore  or you can find restored ones online. Some of them even go to the level of fine furniture and can quickly go for over $5,000.00.

If you prefer the vintage 20 gauge steel esthetic (you know I do!), you can find lots of used, but still great condition slip boxes online in places like eBay or on Craigslist.

I and others have written some advice about other card storage options on a Reddit community targeted at analog zettelkasten in the past.

What do you use? What do you want to use? Are you going to custom build your own? Have you seen other companies like Brodart that still support the manufacturing of these sorts of tools for thought? Please share your ideas and supplies below.

This post was originally published on Chris Aldrich

A Small 10,000+ Annotations Party

A Small 10,000+ Annotations Party
I recently hit the 10,000+ annotations mark on the fantastic Hypothes.is platform, and in celebration, the kind team at Hypothesis sent me a care package with a lovely card, some sticky flags, some stickers, and some chocolate to see me through the next 10,000.

If I’m honest, I get so much value and joy out of annotating online, I should have been the one to send them the care package.

Thanks Hypothes.is! I’ll see you in the margins.

This post was originally published on Chris Aldrich

Looking for books with wider margins for annotations and notes

With the school year starting and a new slew of books to be purchased and read, I’ve been looking for books, particularly popular “classics” or “great books” that are published either with larger margins or even interleaved copies (books in which every other page is blank and meant for writing extensive notes).

Within the bible publishing space (and especially for study bibles), these features seem a lot more common as people want to write more significant marginalia or even full pages of text against or opposite of what they’re reading within the book itself. Given the encouragement many teachers give for students to actively annotate their books for class discussions as well as people commonly doing this, why isn’t it more common for them to recommend or require texts with ample margins?

Almost all of the published mass market paperbacks I see of series like Penguin Classics or Signet classics have the smallest possible margins and no interlinear space for writing notes directly in books. Often hard covers will have slightly larger margins, but generally most publishers are putting 1/2 inch or 3/4″ margins on their classics series (Penguin Classics, Everyman Library, Signet (a paltry 1/4 inch usually), Library of America, Norton Classics, Wordsworth Classics, Dover, etc.)

For those wanting ample margins for active “reading with a pen in hand” are there any publishers that do a great job of wider margins on classics? Which publishers or editions do others like or recommend for this sort of reading?

Are there any book sales platforms that actually list the size of margins of their books? (I never seen one myself.)

What can consumers do to encourage publishers to change these practices?

I’ve seen only a few select titles from very few publishers that do things like this. Examples include:

  • Gladius Books’ Huckleberry Finn
  • Annotate Books’ Marcus Aurelius, which has 1.8″ lined margins
  • The Folio Society has slightly better margins on their texts, but they’re generally larger hardcover collectors’ editions that are dramatically more expensive than is practicable for students on a budget. ($80+ versus $5-10)

If I can’t find anything useful, I’m tempted to self-publish custom versions of wide margin or interleaved books otherwise. Something in the inch to inch and a half margin size for commonly used texts in literature classes should be much more commonplace.

This post was originally published on Chris Aldrich