The Stella Decimal System

The Stella Decimal System, or SDS, organizes the Stella Library of problems by topic. It takes its inspiration from the Dewey Decimal System, which gives numerical call numbers to books. The SDS lives on a spreadsheet. Have a look: SDS is either a list of some 350 four-digit numbers and the corresponding topics, or an alphabetical list of some 350 topics and their corresponding numbers.

The idea behind the SDS is to have a handy list of lots of different categories of mathematical brainteasers and non-routine problems, starting with the little brainteasers that you find on paper placemats in some diners, on up through arithmetic, algebra, geometry, trigonometry and into pre-calculus.

Note that the 350 four-digit numbers are not the call numbers for specific problems. Instead, they indicate categories of problems — problem topics. Each individual problem within a category has its own call number beginning with the four digits, but ending with two decimal places. For instance, the category "tracing networks" has the four-digit call number 1007. Then, the specific problem that asks you to trace a network of three overlapping squares has SDS call number 1007.22. You might also note that the three problems in the 1007 category are not organized in any particular way — they do not progress in difficulty, for instance. For the most part, the two-decimal identifiers were simply assigned as problems were added to the collection.

If you take another look at the numerical list, you will observe that the four-digit numbers starting with 1000 and ending with 1095 are categories for pure brainteaser types — for instance, 1007 tracing networks, 1050 arranging pennies, and 1080 optical illusions.

Starting with 1100, we have categories for problems that can involve numbers, such as 1120 cross-number puzzles, and 1130 magic squares. At 1200 we start seeing logical problems, such as 1210 who has which hat on, 1240 river crossing, and 1260 the handshake problem. Problems involving regular arithmetic begin with 1310. Problems about squares and square roots are at 1330 — and if you check 1330 you will see a cross-reference that more problems can be found at 1680, the category of factorials.

Problems specifically involving calculators are found at 1460-1480. Beginning at 1500 we have categories for problems that are at the edge of algebra — an equation might be useful but is not necessary. An example of such a problem is 1540.34 Aggie's eggs.

Starting with 2000, we see categories for problems that involve algebra, such as 2090 linear expressions, 2211 inequalities with absolute value, 2232 quadratic functions, and 2440 distance rate, time problems. The nifty problem about a train in a tunnel has call number 2440.79. There are 128 four-digit SDS categories for algebra problems — it is a huge subject!

SDS categories in the 3000s involve geometry, such as 3070 supplementary and complementary angles, 3140 three-dimensional problems with congruent triangles, and 3305 regular polygons. The problem about the altitude of a regular octagonal stop sign is 3305.52. There are 93 SDS categories of geometry problems.

At the 4000 level we reach trigonometry. Examples: 4040 graphs of trigonometric functions, 4140 Law of Sines, and 4200 juicy numerical trig problems. The problem about sailing your elegant yacht down the Hudson River has SDS call number 4200.23. There is a small selection of elementary probability problems at 4400-4420.

Using SDS for Your Own Ends

The first big benefit of having a library of problems stored with SDS call numbers is pretty clear. Namely, if you have, say, an Algebra II class that has recently studied logarithms, you can look in the library for the logarithm categories (2730, 2735, and 2740), and browse through what you find, to see what would suit your class. If you are getting your math team ready for a contest and you want them to work on Pythagorean Theorem problems at today's practice, you can pull up all of the 3470 and 3475 problems, print them out, and there is your work session ready to go.

But you can also use SDS the other way around. Suppose you have a book of recreational math problems, or contest problems, or back copies of contests themselves. Suppose you are looking for some really good problems for your geometry class. You browse through the book and you keep saying, "Wow, that would be great for Algebra II" and "Wow, this would be perfect for Trig." But you are looking for geometry problems, so you pass these by — even though next week you might be looking for good Algebra II or Trig problems. Well, you can use the SDS to give those algebra and trig problems call numbers as you find them, put them on filing cards (or on disc), and thus start a library of your own. Use the alphabetical listing of the categories to find the numbers you need, but store the cards in numerical order. If that first problem you saw — the algebra problem you did not want just then — is a word problem involving changing bases of logarithms, you would give it a number starting with 2740, Logarithms, change of base. The decimal part could be anything you like except 31 or 38, which have already been applied to Stella problems in category 2740.

Note: What if you have a counting problem that involves, say, a circle? Now you have a choice: Store it under counting problems, 1342, or under circles, 3500, according to where you feel it best fits.

So, the second use of the SDS is to give you a place to put problems that you have come across that you like, even though you may not use them right away. That is exactly what Stella had in mind when she set up the SDS in the first place. If you find a category that Stella left out, feel free to add a number to the SDS. Library cataloging systems are always designed to expand as the need arises, and SDS has plenty of room for enhancements.