[FoRK] evidence based trig

Dave Long < dave.long at bluewin.ch > on > Thu Jul 6 13:38:32 PDT 2006

>> SOHCAHTOA is a mnemonic? Maybe for an Iroquois.
> Well I've never forgotten it. QED :)

Why memorize mnemonics, when one can always ask the machine?

Let's say one has some unknown trig functions*, foo(x), bar(x), and 
bletch(x); discriminating between the three is a simple matter of 
punching the foo, bar, and bletch buttons on a calculator and examining 
the graphs.

one will be close to unity close to the origin.  That'll be A/H.
(minute angle means that A had better be close to H)
one of the remaining two will run off to infinity.  That'll be O/A.
(O and A can't be any larger than H)
and the last will be a shifted copy of the first.  That'll be O/H.
(O and A components swap depending upon how we measure the angle)

-Dave

* feel free to replace ASCII names with lewis carroll trig notation.

:: :: ::

If, on the other hand, two of them take on values outside of unity, you 
are probably traveling at some significant fraction of c relative to 
your triangle and hence should be looking for hyperbolic functions 
instead.
(are there any relativistic first person shooter engines?)

> It's pretty interesting how much the terms and concepts were used and
> available to anyone (in Ohio!) back in 1901/2.

Seeing as how trig is useful for facilitating both peaceful transfers 
of property (metes and bounds) and violent transfers of property 
(spotting and artillery), I wouldn't be surprised to find the concepts 
used and available even in the Ohio of 1803.  (and used, but maybe not 
so available, in the the India of 503 BC)

On the other hand, some applications of concepts may only seem obvious 
in hindsight, like Galileo's categorical decomposition of motion along 
horizontal (adjacent) and vertical (opposite) projections -- or was 
renaissance artillery (at least among the turks) advanced enough that 
it was simply a matter of showing how common practice could work in 
theory?


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