Last week, I was visiting my mom, and hanging some Christmas lights for her, when I noticed this piece of computing history on a desk in her back room. What you see there is a Texas Instruments TI-1250 "pocket calculator", circa 1975. My mom bought this one to handle her checkbook and such back then, and has used it ever since. If you look at the photo, you'll see it's a pretty basic machine... it adds, subtracts, multiplies and divides. But the big news, what made it "fully loaded" (according to http://www.datamath.org/BASIC/TI-1200/TI-1250.htm, a site dedicated to Texas Instruments calculators, with a ton of information on many, many models), are the four M buttons which allow you to store numbers in memory so you can then use them in another equation. Pretty simple stuff compared to the modern graphing calculators and such that a typical schoolkid is carrying around today. But back when she bought this, I remember being amazed that this little box could do what it did. Bear in mind that when I was in 8th grade chemistry, I was taught how to use a slide rule! For those of you too young to know, that was a basic mechanical computer that consisted of several sliding pieces marked with numbers that, when manipulated by someone who knew what they were doing, could perform some pretty elaborate math (http://en.wikipedia.org/wiki/Slide_rule). Watch any documentary about the space program or even the movie Apollo 13 and you'll see that slide rules were an intrinsic part of NASA operations.
The funny thing is, as I went forward in school, I of course bought and used much more sophisticated calculators, which included such things as trigonometric functions, square roots, scientific notation, etc., as well as a specialized "foot and inch" calculator designed specifically for the building trades. All of these were indispensable tools during my career as a theatre technical director, but while I still own a couple of pretty capable calculators, the overwhelming majority of my day to day needs could be met by that old TI-1250 these days.
Now, to bring this all back to bikes... take a look here:
where you will find a page by the late, great Sheldon Brown about using a slide rule to figure out chain ring and sprocket combinations to achieve a specific gear ratio. I've never tried it, but it seems pretty straightforward... assuming you have a slide rule!