kirby urner wrote:
However, one thing calculators lack over the old wood pulp
textbooks are trig tables with multiple rows showing a lot of
data at the same time. Their small "chat window" does not
permit much data to be seen at one time.
Back in the day, a student could run her finger down the
rows, as the number of angular degrees increase from
0 to 60 and onward to 90, perhaps all the way around to
360.
Going across the row, one would have sine and cosine,
perhaps tangent. Having all the data visible at once, or spread
across a few pages, inspired some insights and understanding,
as one could see the trends in the numbers, plus these
"click stop" rows where the numbers would suddenly be
super easy, like 1/2 and 1/2 for both sine and cosine.
There is a fascinating article on the history of mathematical tables in
the latest ACM.
http://cacm.acm.org/opinion/articles/81487-be-careful-what-you-wish-for/fulltext
People made careers out of producing these tables! They hired armies
of human calculators (all women) grinding out these numbers.
Made me think of my first experiences with the sine function. I used
one of these books to make a giant plot of a sine wave. I was
fascinated by the shape, and the beauty of it. I practiced drawing sine
waves like an artist would, looking ahead at the point where you want
your pencil to go. I had a question which didn't get answered until
years later. Why do generators make sine waves? I was familiar with
the construction of generators, having read about them, and taken one
apart at age 14, working on my first car. I had an oscilloscope, with
which I could see the sine waves coming out of the outlet in my
bedroom. But it was a mystery how something so crude as a generator
could make something as precise and beautiful as a sine wave. Python
could have answered my question.
Maybe at age 14, instead of spending my time hanging out with the
juvenile delinquents in my neighborhood, I could have been playing with
simulations of power systems, and seeing how waveforms are made up of
sinusoidal components. I was into amateur radio at the time, so I knew
about modulation and sidebands, but again, so many unanswered
questions. How can you *add* power to a transmitted wave by simply
twiddling the voltage on the grid of a vacuum tube? Again, Python would
have helped.
The contents of trigtable.txt:
0 1.000000000 0.000000000 0.000000e+00
1 0.999847695 0.017452406 1.745506e-02
2 0.999390827 0.034899497 3.492077e-02
3 0.998629535 0.052335956 5.240778e-02
4 0.997564050 0.069756474 6.992681e-02
5 0.996194698 0.087155743 8.748866e-02
6 0.994521895 0.104528463 1.051042e-01
7 0.992546152 0.121869343 1.227846e-01
8 0.990268069 0.139173101 1.405408e-01
9 0.987688341 0.156434465 1.583844e-01
10 0.984807753 0.173648178 1.763270e-01
11 0.981627183 0.190808995 1.943803e-01
12 0.978147601 0.207911691 2.125566e-01
13 0.974370065 0.224951054 2.308682e-01
14 0.970295726 0.241921896 2.493280e-01
15 0.965925826 0.258819045 2.679492e-01
16 0.961261696 0.275637356 2.867454e-01
17 0.956304756 0.292371705 3.057307e-01
18 0.951056516 0.309016994 3.249197e-01
19 0.945518576 0.325568154 3.443276e-01
20 0.939692621 0.342020143 3.639702e-01
21 0.933580426 0.358367950 3.838640e-01
22 0.927183855 0.374606593 4.040262e-01
23 0.920504853 0.390731128 4.244748e-01
24 0.913545458 0.406736643 4.452287e-01
25 0.906307787 0.422618262 4.663077e-01
26 0.898794046 0.438371147 4.877326e-01
27 0.891006524 0.453990500 5.095254e-01
28 0.882947593 0.469471563 5.317094e-01
29 0.874619707 0.484809620 5.543091e-01
30 0.866025404 0.500000000 5.773503e-01
31 0.857167301 0.515038075 6.008606e-01
32 0.848048096 0.529919264 6.248694e-01
33 0.838670568 0.544639035 6.494076e-01
34 0.829037573 0.559192903 6.745085e-01
35 0.819152044 0.573576436 7.002075e-01
36 0.809016994 0.587785252 7.265425e-01
37 0.798635510 0.601815023 7.535541e-01
38 0.788010754 0.615661475 7.812856e-01
39 0.777145961 0.629320391 8.097840e-01
40 0.766044443 0.642787610 8.390996e-01
41 0.754709580 0.656059029 8.692867e-01
42 0.743144825 0.669130606 9.004040e-01
43 0.731353702 0.681998360 9.325151e-01
44 0.719339800 0.694658370 9.656888e-01
45 0.707106781 0.707106781 1.000000e+00
46 0.694658370 0.719339800 1.035530e+00
47 0.681998360 0.731353702 1.072369e+00
48 0.669130606 0.743144825 1.110613e+00
49 0.656059029 0.754709580 1.150368e+00
50 0.642787610 0.766044443 1.191754e+00
51 0.629320391 0.777145961 1.234897e+00
52 0.615661475 0.788010754 1.279942e+00
53 0.601815023 0.798635510 1.327045e+00
54 0.587785252 0.809016994 1.376382e+00
55 0.573576436 0.819152044 1.428148e+00
56 0.559192903 0.829037573 1.482561e+00
57 0.544639035 0.838670568 1.539865e+00
58 0.529919264 0.848048096 1.600335e+00
59 0.515038075 0.857167301 1.664279e+00
60 0.500000000 0.866025404 1.732051e+00
61 0.484809620 0.874619707 1.804048e+00
62 0.469471563 0.882947593 1.880726e+00
63 0.453990500 0.891006524 1.962611e+00
64 0.438371147 0.898794046 2.050304e+00
65 0.422618262 0.906307787 2.144507e+00
66 0.406736643 0.913545458 2.246037e+00
67 0.390731128 0.920504853 2.355852e+00
68 0.374606593 0.927183855 2.475087e+00
69 0.358367950 0.933580426 2.605089e+00
70 0.342020143 0.939692621 2.747477e+00
71 0.325568154 0.945518576 2.904211e+00
72 0.309016994 0.951056516 3.077684e+00
73 0.292371705 0.956304756 3.270853e+00
74 0.275637356 0.961261696 3.487414e+00
75 0.258819045 0.965925826 3.732051e+00
76 0.241921896 0.970295726 4.010781e+00
77 0.224951054 0.974370065 4.331476e+00
78 0.207911691 0.978147601 4.704630e+00
79 0.190808995 0.981627183 5.144554e+00
80 0.173648178 0.984807753 5.671282e+00
81 0.156434465 0.987688341 6.313752e+00
82 0.139173101 0.990268069 7.115370e+00
83 0.121869343 0.992546152 8.144346e+00
84 0.104528463 0.994521895 9.514364e+00
85 0.087155743 0.996194698 1.143005e+01
86 0.069756474 0.997564050 1.430067e+01
87 0.052335956 0.998629535 1.908114e+01
88 0.034899497 0.999390827 2.863625e+01
89 0.017452406 0.999847695 5.728996e+01
90 0.000000000 1.000000000 1.633124e+16
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