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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

714.0. "sin(cos(x)) = x etc." by IOSG::DEMORGAN () Fri Jun 05 1987 13:52

    Using a pocket calculator, starting with some reasonable number,
    and iterating, it can be shown (at least to the limits of my old
    Casio fx-101) that
    
    	sin(cos(x)) = x = 0.68481969
    
    	cos(sin(y)) = y = 0.76816915
    
    	tan(sin(z)) = tan(cos(tan(cos(z)))) = z = 1.5570858
    
    There are probably more such relationships. Does anybody know any
    analytical solutions?
    
    Richard De Morgan.
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714.1Like magnets...AKQJ10::YARBROUGHWhy is computing so labor intensive?Mon Jun 08 1987 12:396
The numbers in the previous note are known as *attractors* - note that the 
last one is obtained from two unrelated formulae - and there is some theory 
about them. If I recall aright, Doug Hofstadter discussed them in his 
Scientific American column and in "Metamagical Themas", his recent book.

Lynn Yarbrough