In article <3330F524.240C@ccvax.sinica.edu.tw>, Ko-Wei Lih <email@example.com> writes: |> Does any one know the etymology of the word "totient" which is used in |> "Euler's totient function"? Any historical background of why Euler used |> this word is also welcome.
Euler certainly didn't use the word. According to Graham, Knuth and Patashnik, "Concrete Mathematics", the word was invented by J.J. Sylvester, "a British mathematician who liked to invent new words". The reference they give is to a paper from 1883: "On the number of fractions contained in any 'Farey series' of which the limiting number is given", reprinted in Sylvester's "Collected Mathematical Papers", vol. 4, 101-109.
Robert Israel firstname.lastname@example.org Department of Mathematics (604) 822-3629 University of British Columbia fax 822-6074 Vancouver, BC, Canada V6T 1Y4