[Edu-sig] using Python as a calculator
Edward Cherlin
echerlin at gmail.com
Fri Apr 9 18:41:16 CEST 2010
[sigh]
Do math tables in a math array language.
degrees =. i. 91 NB. 0..90
radians =. degrees * o. % 180
table =. |: degrees, 1 2 3 o./ radians
where
=. is assignment
i. creates a list of consecutive numbers starting at 0.
NB. is the comment marker
o. x is pi times x
% x is reciprocal of x, so o. % 180 is pi/180
|: is transpose
, appends an array to another. It turns a list into a table in order
to match dimensions.
1 2 3 o. x gives sine, cosine, tangent of x
/ creates a table with the given function (o.) applied to two list arguments
The result is a 91 row, 4 column table of angles and trig function values.
I can easily give you a short sequence of lessons leading to this
level, introducing some other arithmetic, transcendental, and
array-handling functions along the way, and a little more about
operating on functions to define new functions.
J is no-charge software from JSoftware.com. We are discussing the
possibility of a GPLed version.
When you do such function tables, it is extremely helpful to show the
first differences. The differences of sine are approximately
proportional to cosine, and of cosine are proportional to the
negatives of sine.
On Thu, Apr 8, 2010 at 10:43, kirby urner <kirby.urner at gmail.com> wrote:
> I think Guido was wise to start his tutorial by showing how we
> might use Python as a calculator.
>
> We might assume many students in this day and age are quite
> familiar with this device, and even if they're not, the text might
> project one, show a picture on the screen, if what these things
> used to look like (still do).
>
> 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.
>
> Calculators don't give us that kind of output, but earlier office
> computing machines did have paper i/o, called a tape, usually
> a scroll mounted on a spool and fed through a small printer.
>
> As one added numbers, one printed to tape, perhaps a running
> total. The tape itself was a valuable item (especially once it
> had the data on it).
>
> Large computers came with line printers that hit on continuous
> feed paper with holes along both sides, often with green and
> white stripes. I will not try to recapitulate the long history
> of printing devices, except to point out that computers
> inherited them while slide rules and calculators did not.
>
> The equivalent in Python is stdout and/or some file in storage,
> on the hard drive or memory stick. The program output
> shown below would be an example of this kind of i/o.
>
> Notice that unless a file name is given (optional), the data
> is to stdout.
>
> I'm going to do a full 90 degrees, just to remind myself of
> the patterns students got in the old days, before trig tables
> were replaced with calculators, much as dial watches were
> replaced with digital ones (not necessarily a smart move
> in all cases).
>
>>>> imp.reload(newprint)
> <module 'newprint' from 'C:\Python26\lib\site-packages\newprint.py'>
>>>> newprint.trigtable(range(91), "trigtable.txt")
>
> 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
>
> Here's the print function I used to generate the above.
>
> print("{0:>5g} {1:.9f} {2:.9f} {3:e}".format(
> row, cos(theta), sin(theta),tan(theta)),
> end="\n", file= thefile)
>
> My module starts with:
>
> from __future__ import printfunction
>
> which is why I get to use this in 2.6
>
> So why use Python as a calculator again? Because it's more like
> an old office machine with a tape, and that restores some of what
> was lost when lookup tables went out of style. I should do log10
> next, using range with a step or something.... Also, the trig tape
> should probably be 0-360 but I didn't want to waste paper. :)
>
> Kirby
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>
--
Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://www.earthtreasury.org/
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