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 http://www.geocities.com/Paris/Rue/1861/arithme3.html#surd "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 http://jeff560.tripod.com/s.html "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" (OED2). "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 http://mathforum.org/dr.math/
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