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In his book Control System Design, Bernard Friedland writes (section 4.2, page 115):

The roots of the denominator [of a rational function] are called the poles of the transfer function because $H(s)$ becomes infinite at these complex frequencies and a contour map of the complex plane appears as if it has poles sticking up from these points.

Is there any historical legitimacy to this explanation of the origin of the word "pole" to describe a root of the denominator of a rational function?

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I always thought that poles come from electric poles which are singularities of the electric force, that is, a place where a function becomes infinite. –  lhf Mar 21 '12 at 10:54
    
I don't see any direct math-history connection when looking at: etymonline.com/index.php?term=pole&allowed_in_frame=0, or it's very convoluted? lhf's logic seems sound? –  Mr_CryptoPrime Mar 21 '12 at 11:49
    
@lhf What do you mean by 'electric pole'? a point charge? –  Tobin Fricke Mar 21 '12 at 12:45
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The word 'pole' has an entry in Jeff Miller's list (which is oft-referenced around here): jeff560.tripod.com/p.html –  dls Mar 21 '12 at 15:11
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This question also has other references to check: math.stackexchange.com/questions/19397/… –  dls Mar 21 '12 at 15:14

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