Infinirule is a virtual slide rule. It transcends the limitations of real physical slide rules by allowing variable precision—just keep zooming in to get more—and automatically wrapping scales around—like a circular slide rule, but without the bulk. And though it only shows four scales at a time, you can select any combination of the available scale types.
Like most slide rules, Infinirule consists of 3 parts which can move relative to each other: the top 2 scales are part of the body, the bottom 2 are the slide, and there is also the cursor, with a hairline for taking accurate readings. The top two scales move together, as do the bottom two. Dragging the body moves the entire rule left or right, while dragging the slide only moves that. Use two fingers in either the body or the slide to pinch-zoom the rule horizontally to adjust the precision. Dragging in the space below or above the rule scales engages “precision” moving at 1/10th speed, for fine adjustments. You can move either the scales or the cursor in this way.
The padlock icon lets you lock the slide to the body, to prevent accidental movement of the former relative to the latter while adjusting your view. When the padlock is open, the slide can be freely moved relative to the body.
Tap on a scale name to bring up a menu that lets you select the scale to show in that position. Long-tap on the cursor to copy/paste scale readings to/from the clipboard.
On Android 3.0 or later, the following options should be directly available in the action bar at the top of the screen. On earlier versions of Android, press the menu button to bring them up:
A slide rule is an example of an analog computer. Unlike the (nowadays) more common digital computer, which uses a limited set of physical states (e.g. “on” and “off” electrical signals) to encode digits of numbers, analog ones perform computations by directly manipulating continuous physical quantities. In the case of a slide rule, the quantities are lengths along graduated scales. The basic operation is adding and subtracting of lengths, by sliding one scale relative to another before taking a reading. However, by using suitable scale graduations, it is possible to perform more complicated operations than just adding and subtracting numbers; for example, the most basic slide rule scale is logarithmic, which allows you to perform multiplication and division of two numbers by adding and subtracting their logarithms.
Analog computers used to be common back in the early part of the 20th century, when digital technology was expensive. And slide rules were easier to carry around. But where the digital computers could work on numbers with long strings of 7 or more digits (giving correspondingly high precision), analog ones typically could only manage about 3 digits of precision. Larger slide rules could go to more digits, at the expense of becoming more unwieldy (and expensive and difficult to make); Infinirule gives the same effect by letting you zoom in to the scales.
Consider a simple example: what’s 1.2 multiplied by 3.4? This can be solved by using just the centre two default scales, labelled x (on the body) and y (on the slide).
First of all, drag the lower scale so the “1” graduation on the slide is opposite
the “1.2” graduation (second longer unmarked graduation between “1” and “2”)
on the body, thus:
(Feel free to pinch-zoom in to get more accurate positioning.)
Now, if necessary, drag the body (so the slide moves with it) until
the “3.4” graduation is visible on the slide. Then move the cursor so that
its hairline coincides with this graduation, thus:
Now you can simply read off the answer from where the cursor hairline crosses the body scale. In this case, it is slightly under 4.1; if you zoom in enough, you should be able to see that the answer is 4.08.
Now, how would you compute 12 times 34? In fact, this corresponds to the same scale reading, because these two scales have no explicit decimal point, and wrap around when they run off the end; you have to work out where the decimal goes by estimating the magnitude of the result. 1.2 × 3.4 should be closer to 1 × 3 = 3 rather than 0.3 (or less) or 30 (or more), while 12 × 34 should be closer to 10 × 30 = 300 rather than 30 (or less) or 3000 (or more), therefore the correct answer must be 408.
OK, now what is 1.2 divided by 3.4? To work this out, move the cursor
hairline to 1.2 on the body scale, and then move the slide so the 3.4
mark on that also coincides with the cursor hairline:
Then drag the body as necessary to make the 1.0 graduation visible on
the slide scale. Move the cursor hairline to this mark (being careful not
to disturb the position of the slide relative to the body):
Now, 1.2 ÷ 3.4 should be close to 1 ÷ 3 which is about 0.3. Therefore, the value on the body scale under the hairline must be slightly over 0.35, rather than 3.5 or anything else. To 3 figures, it is approximately 0.353.
Scales are named in Infinirule according to the mathematical formula defining them, not according to the traditional slide rule scale labels. Here is a table of correspondences between traditional labels and Infinirule names (names shown in red are descending scales, rest are ascending):
Traditional Label | Infinirule Name | Wrap |
---|---|---|
A | x2 | yes |
B | y2 | yes |
C | y | yes |
CF | πy | yes |
CI | 1/y | yes |
CIF | 1/(πy) | yes |
D | x | yes |
DF | πx | yes |
DI | 1/x | yes |
DIF | 1/(πx) | yes |
K | x3 | yes |
L | log10 x | yes |
Ln | ln x | no |
LL3 | exp(x) | no |
LL2 | exp(0.1x) | no |
LL1 | exp(0.01x) | no |
LL0 | exp(0.001x) | no |
exp(-x) | no | |
exp(-0.1x) | no | |
exp(-0.01x) | no | |
exp(-0.001x) | no | |
N3 | 10**x | no |
N2 | 10**(0.1x) | no |
N1 | 10**(0.01x) | no |
N0 | 10**(0.001x) | no |
10**(-x) | no | |
10**(-0.1x) | no | |
10**(-0.01x) | no | |
10**(-0.001x) | no | |
acos° x > 5.7° | no | |
0.8° < acos° (0.001x + 0.99) < 8° | no | |
acosh x | no | |
acosh 10x | no | |
R1 | √x | no |
R2 | √10x | no |
S | asin° x > 5.7° | no |
Sh | asinh 0.1x | no |
Sh | asinh x | no |
asinh 10x | no | |
ST | 0.57° < asin° x ≤ 5.7° | no |
0.57° < atan° x ≤ 5.7° | no | |
T | atan° x > 5.7° | no |
atanh 0.01x | no | |
Th | atanh 0.1x | no |
Note the following points:
For more info about slide rules, visit the International Slide Rule Museum at sliderulemuseum.com.