Subject: RE: [MATHEDCC] square root of -1 history
From: Lindsey, Dr. Charles (clindsey@fgcu.edu)
Date: Mon Jan 24 2000 - 10:52:38 EST
See "An Imaginary Tale: The story of the square root of -1" by Paul J. Nahin
for a complete discussion of the origin of imaginary numbers. (Princeton
Univ. Press, 1998, ISBN 0691027951)
It is also worth mentioning the contribution of Rafael Bombelli, in his
*Algebra* of 1572 (approx.). Bombelli first explicitly stated the correct
rules of algebraic operation with square roots of negative numbers (although
he did not use the term "imaginary" for them).
Chuck Lindsey, Ph.D. clindsey@fgcu.edu
Director of General Education
Associate Professor and Program Leader, Mathematics
Florida Gulf Coast University
10501 FGCU Blvd South
Fort Myers, FL 33965-6565
Phone: (941) 590-7168 FAX: (941) 590-7200
http://itech.fgcu.edu/faculty/clindsey
> -----Original Message-----
> From: mahlerp@middlesex.cc.ma.us [SMTP:mahlerp@middlesex.cc.ma.us]
> Sent: Friday, January 21, 2000 7:30 PM
> To: haehl@kcmetro.cc.mo.us
> Cc: mathedcc@archives.math.utk.edu
> Subject: Re: [MATHEDCC] square root of -1 history
>
> haehl@kcmetro.cc.mo.us writes:
> >Hi all,
> >
> >I have 2 questions.
> >
> >1. Does anyone know what mathematicians first studied the square root of
> >-1
> >and when it was first called an imaginary number?
> >
> ...
> >
> >
> >Martha
>
>
> Florian Cajori "A History of Mathematical Notations" discusses "Symbolism
> for Imaginaries and Vector Analysis". (An great book to own. Thankfully
> this 1920s book is now back in print.)
>
> "The earliest mathematician seriously to consider imaginaries and to
> introduce them in the expression for the roots of equations was H.
> Cardan." He used these in the Ars magna in 1545, but not with the radix
> symbol. 5 + sqrt(-15) was 5p:Rm:15, for example.
>
> In 1629 Albert Girard uses the radix for sqrt(-2). ... Before Euler the
> sign sqrt(-1) (with the radix, and using 1) as distinct from sqrt(-a)
> seldom, if ever, occurs.
>
> It was Euler who first used the letter i for sqrt(-1) in a memoir in 1777.
>
> Phil Mahler
>
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