Re: History of trigonometry

Nick wrote:
"Ken Pledger" <ken.pledger@xxxxxxxxxxxxx> wrote in message
news:ken.pledger-E6DD48.11304703012007@xxxxxxxxxxxxxxxxxxxxx
In article
<2386070.1166882761600.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
zeros <nimzeros@xxxxxxxxx> wrote:

....
When did someone define the sine of an angle greater than 90 degrees?

I think this may be happened in 17c. But I can't find any record about my
question....


It's an interesting question, which most popular historians of
mathematics scarcely mention.

In fact, http://www-history.mcs.st-andrews.ac.uk/Biographies/Euler.html says
that:

"He made large bounds forward in the study of modern analytic geometry and
trigonometry where he was the first to consider sin, cos etc. as functions
rather than as chords as Ptolemy had done."

http://www-history.mcs.st-andrews.ac.uk/HistTopics/Trigonometric_functions.html#76
says that:

"The first actual appearance of the sine of an angle appears in the work of
the Hindus."

"Chapters of Copernicus's book giving all the trigonometry relevant to
astronomy was published in 1542 by Rheticus. Rheticus also produced
substantial tables of sines and cosines which were published after his
death. In 1533 Regiomontanus's work De triangulis omnimodis was published.
This contained work on planar and spherical trigonometry originally done
much earlier in about 1464. The book is particularly strong on the sine and
its inverse."

See reference for more.

Nick

Sine, cosine, and tangent may be elementary functions, I am wondering
if there are these slightly less elementary functions that are similar
to sinecosine and tangent.

Basically I've heard that sine and cosine can be described by the
evolving coordinates of an unhinged regular triangle, where it goes
from being a triangle to a straight line, and there's a ratio, perhaps
unity, between the change of the arc of the angle AB and angle BC, so
that it unfolds in this graceful manner and the endpoint happens to go
through a path that traces half a period of the sine function, or
something along those lines. That does describe a periodic function,
with constant period the perimeter. Such a thing obviously exists,
questions arise as to the surrounding framework and whether otherwise
more complicated expressions could be reduced to these families of
periodic functions, with irregular polygons and various arc change
ratios. Obviously they could be represented as sums of sine waves.

Where that is so, is there a similar notion to trigonometry for
unfolding regular n-gons, n-gonometry? How about a 3-D or n-D analog
for pyramidometry and n-hedrometry? I figure these are quite well
explained somewhere. Where can I learn more about these things and
their directions of development?

Basically my question here is: what's 4-gonometry. Why is
trigonometry called trigonometry? I understand it's about the ratio of
sides of right triangles.

Ross

.

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