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Date: 05/17/2000 at 22:40:10
From: Kyle Flaspohler
Subject: Square root 

Where does the term "surd" for square root come from? Is it because 
they are "absurd" numbers, and don't really make any sense?

Date: 06/20/2000 at 16:31:32
From: Doctor Sandi
Subject: Re: Square root 

Hi Kyle,

I have found two definitions of SURDS and I'll repeat them here. The 
first is from the following Web page:

   Origins of some Math terms - Pat Ballew   

"SURD - The original meaning of surd was mute, or voiceless. The word 
still retains that meaning today in phonetics for an unvoiced 
consonant (as opposed to a voiced consonant, a sonant). The reference 
is to a root that could not be expressed (spoken) as a rational 
number. It has been reported that al-Khowarizmi [see algebra] referred 
to rationals and irrationals as sounded and unsounded in his writings. 
When these were translated into Latin in the 12th century, the word 
surdus was used."

The second definition is from the following Web page:

   Earliest Known Uses of Some of the Words of Mathematics (S) -
   Jeff Miller   

"According to Smith (vol. 2, page 252), al-Khowarizmi (c. 825) 
referred to rational and irrational numbers as 'audible' and 
'inaudible', respectively. 

"The Arabic translators in the ninth century translated the Greek 
rhetos (rational) by the Arabic muntaq (made to speak) and the Greek 
alogos (irrational) by the Arabic asamm (deaf, dumb). See e.g. 
W. Thomson, G. Junge, The Commentary of Pappus on Book X of Euclid's 
Elements, Cambridge: Harvard University Press, 1930 [Jan Hogendijk].

"This was translated as surdus ("deaf" or "mute") in Latin. 

"As far as is known, the first known European to adopt this 
terminology was Gherardo of Cremona (c. 1150). 

"Fibonacci (1202) adopted the same term to refer to a number that has 
no root, according to Smith.

"Surd is found in English in Robert Recorde's The Pathwaie to 
Knowledge (1551): "Quantitees partly rationall, and partly surde" 

"According to Smith (vol. 2, page 252), there has never been a general 
agreement on what constitutes a surd. It is admitted that a number 
like sqrt 2 is a surd, but there have been prominent writers who have 
not included sqrt 6, since it is equal to sqrt 2 X sqrt 3. Smith also 
called the word surd "unnecessary and ill-defined" in his Teaching of 
Elementary Mathematics (1900). 

"G. Chrystal in Algebra, 2nd ed. (1889) says that '...a surd number is 
the incommensurable root of a commensurable number,' and says that 
sqrt e is not a surd, nor is sqrt (1 + sqrt 2)."

Hope this has helped,
- Doctor Sandi, The Math Forum   
Associated Topics:
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Middle School Definitions
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