[Edu-sig] using Python as a calculator

[David MacQuigg]

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
>