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From: METH@usc-isi.arpa
Newsgroups: net.micro
Subject: Series for Pi and Other Trig Oddities
Message-ID: <1043@brl-tgr.ARPA>
Date: Thu, 26-Dec-85 09:24:35 EST
Article-I.D.: brl-tgr.1043
Posted: Thu Dec 26 09:24:35 1985
Date-Received: Sat, 28-Dec-85 01:42:01 EST
Sender: news@brl-tgr.ARPA
Lines: 23


     My  formula  for  pi,  while  correct,  was  pointed  out  by 
LINDSAY@TL-20B.ARPA to be very, very slowly converging.

     I have seen on the net other,  more quickly converging series 
such as:

     pi/4 = 4*arctan(1/5) - arctan(1/239)

     I  am FASCINATED by the fact that this equality holds.   What 
is special about these two angles to give such an EXACT result.

     Other  examples  of  these  unexpected  rational  results  of 
combinations of functions with irrational solutions  abound,  such 
as

     cos(20degrees)*cos(40degrees)*cos(80degrees) = 1/8

     Does  anyone have mathematical insight as to why these things 
are true?

-Sheldon Meth (METH@ISIA.ARPA)
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