Low-Tech Math

CIRCULAR SLIDE RULES

Slide rules are a more robust way to do math. Slide rules are not dependent on energy infrastructure. I have also found mine to help me visualize numbers. I like my slide rules that help calculate dates, based on the 28-year repeating cycle, but my most helpful slide rule is my huge, 8-inch Binary Slide Rule.

I once read that there were some inaccuracies on it, but that the “clutch” of the pivot arms was its most important contribution to technology.

These are the numbers that are helpful to make one’s own slide rule. This first table gives the angles of the circle at which each Log value of N is located.

American History Gilson Binary Circular Slide Rule

Angle Log N N
0 0 1
36 0.1 1.26
72 0.2 1.58
108 0.3 2.00
144 0.4 2.51
180 0.5 3.16
216 0.6 3.98
252 0.7 5.01
288 0.8 6.31
324 0.9 7.94
360 1 10.00

This table gives the interval around the circle between each .1 or 36 degree value.

Angle Log N N
36.00 0.10 1.26
39.60 0.11 1.29
43.20 0.12 1.32
46.80 0.13 1.35
50.40 0.14 1.38
54.00 0.15 1.41
57.60 0.16 1.45
61.20 0.17 1.48
64.80 0.18 1.51
68.40 0.19 1.55
72.00 0.20 1.58

This table reverses the basis and gives the degree of the circle at which each integer is located.

N Log N Angle
1 0 0.0
2 0.3010 108.4
3 0.4771 171.8
4 0.6021 216.7
5 0.6990 251.6
6 0.7782 280.1
7 0.8451 304.2
8 0.9031 325.1
9 0.9542 343.5
10 1 360.0

I never learned about e or natural logs in school, but I finally learned how nifty it is from my Binary Slide Rule.

Each column makes up its own full circle and each row makes a column on the slide rule. Each column could have its own circle, or they could make a spiral.

0.001 0.01 0.1 1 10
1 1.00100 1.01005 1.10517 2.71828 22,026
2 1.00200 1.02020 1.22140 7.38906 485,165,195
3 1.00300 1.03045 1.34986 20.086 1.07E+13
4 1.00401 1.04081 1.49182 54.598 2.35E+17
5 1.00501 1.05127 1.64872 148.41 5.18E+21
6 1.00602 1.06184 1.82212 403.43 1.14E+26
7 1.00702 1.07251 2.01375 1,097 2.52E+30
8 1.00803 1.08329 2.22554 2,981 5.54E+34
9 1.00904 1.09417 2.45960 8,103 1.22E+39
10 1.01005 1.10517 2.71828 22,026 2.69E+43
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