Re: History of trigonometry

Ross A. Finlayson wrote:
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
---
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.

May be the tetrahedronometry.It should include dihedrals and trihedral
"solid" angles.Unfortunately, this 3D counterpart did not develop so
well or used so much like plane trigonometry.It could have involved
quaternions.

Why is trigonometry called trigonometry?

Very clear from its Sanskrit roots: Tria (three,sounds are similar in
English,German and French),Kona (gonio is angle),Matra (size,measure
or unit).These three currently used Indian words are common parlance.

Narasimham

Ross

.

Relevant Pages

  • History of trigonometry
    ... When did someone define the sine of an angle greater than 90 degrees? ... "Chapters of Copernicus's book giving all the trigonometry relevant to ... That does describe a periodic function, ...
    (sci.math)
  • Re: History of trigonometry
    ... When did someone define the sine of an angle greater than 90 degrees? ... "Chapters of Copernicus's book giving all the trigonometry relevant to ... That does describe a periodic function, ...
    (sci.math)
  • Re: History of trigonometry
    ... When did someone define the sine of an angle greater than 90 degrees? ... "Chapters of Copernicus's book giving all the trigonometry relevant to ... astronomy was published in 1542 by Rheticus. ...
    (sci.math)
  • Re: Sine code for ANSI C
    ... >> compute the sine of small arguments quickly, but if it has to take ... > angle is greater than pi. ... All the library writer knows is that there's little *precision* ... small arguments it radians are easy to compute. ...
    (comp.lang.c)
  • Re: Calculating Pi
    ... when you take the sine of a small angle, ... This method leads naturally to ... then sin x is very nearly 0. ...
    (sci.math)