Imaginary unit (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Imaginary unit" in English language version.

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5books.google.com

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1utoronto.ca

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1hmc.edu

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americanscientist.org

Silver, Daniel S. (November–December 2017). "The New Language of Mathematics". American Scientist. 105 (6): 364–371. doi:10.1511/2017.105.6.364.

archive.org

Stubbings, George Wilfred (1945). Elementary vectors for electrical engineers. London: I. Pitman. p. 69.
Boas, Mary L. (2006). Mathematical Methods in the Physical Sciences (3rd ed.). New York [u.a.]: Wiley. p. 49. ISBN 0-471-19826-9.
Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics. John Wiley & Sons. pp. 439–445. ISBN 978-0-471-54397-8.

books.google.com

Doxiadēs, Apostolos K.; Mazur, Barry (2012). Circles Disturbed: The interplay of mathematics and narrative (illustrated ed.). Princeton University Press. p. 225. ISBN 978-0-691-14904-2 – via Google Books.
Bunch, Bryan (2012). Mathematical Fallacies and Paradoxes (illustrated ed.). Courier Corporation. p. 31-34. ISBN 978-0-486-13793-3 – via Google Books.
Kramer, Arthur (2012). Math for Electricity & Electronics (4th ed.). Cengage Learning. p. 81. ISBN 978-1-133-70753-0 – via Google Books.
Picciotto, Henri; Wah, Anita (1994). Algebra: Themes, tools, concepts (Teachers' ed.). Henri Picciotto. p. 424. ISBN 978-1-56107-252-1 – via Google Books.
Nahin, Paul J. (2010). An Imaginary Tale: The story of " $i$ " [the square root of minus one]. Princeton University Press. p. 12. ISBN 978-1-4008-3029-9 – via Google Books.

davidhestenes.net

The interpretation of the imaginary unit as the ratio of two perpendicular vectors was proposed by Hermann Grassmann in the foreword to his Ausdehnungslehre of 1844; later William Clifford realized that this ratio could be interpreted as a bivector.
Hestenes, David (1996). "Grassmann's Vision" (PDF). In Schubring, G. (ed.). Hermann Günther Graßmann (1809–1877). Boston Studies in the Philosophy of Science. Vol. 187. Springer. pp. 243–254. doi:10.1007/978-94-015-8753-2_20. ISBN 978-90-481-4758-8.

doi.org

Silver, Daniel S. (November–December 2017). "The New Language of Mathematics". American Scientist. 105 (6): 364–371. doi:10.1511/2017.105.6.364.
The interpretation of the imaginary unit as the ratio of two perpendicular vectors was proposed by Hermann Grassmann in the foreword to his Ausdehnungslehre of 1844; later William Clifford realized that this ratio could be interpreted as a bivector.
Hestenes, David (1996). "Grassmann's Vision" (PDF). In Schubring, G. (ed.). Hermann Günther Graßmann (1809–1877). Boston Studies in the Philosophy of Science. Vol. 187. Springer. pp. 243–254. doi:10.1007/978-94-015-8753-2_20. ISBN 978-90-481-4758-8.
Euler expressed the partial fraction decomposition of the trigonometric cotangent as ${\textstyle \pi \cot \pi z={\frac {1}{z}}+{\frac {1}{z-1}}+{\frac {1}{z+1}}+{\frac {1}{z-2}}+{\frac {1}{z+2}}+\cdots .}$
Varadarajan, V. S. (2007). "Euler and his Work on Infinite Series". Bulletin of the American Mathematical Society. New Series. 44 (4): 515–539. doi:10.1090/S0273-0979-07-01175-5.
Ivan, M.; Thornber, N.; Kouba, O.; Constales, D. (2013). "Arggh! Eye factorial . . . Arg(i!)". American Mathematical Monthly. 120: 662–665. doi:10.4169/amer.math.monthly.120.07.660. S2CID 24405635.
Sloane, N. J. A. (ed.). "Decimal expansion of the real part of i!", Sequence A212877; and "Decimal expansion of the negated imaginary part of i!", Sequence A212878. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

hmc.edu

math.hmc.edu

"i to the i is a Real Number – Math Fun Facts". math.hmc.edu. Retrieved 22 August 2024.

oed.com

"imaginary number". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)

oeis.org

Ivan, M.; Thornber, N.; Kouba, O.; Constales, D. (2013). "Arggh! Eye factorial . . . Arg(i!)". American Mathematical Monthly. 120: 662–665. doi:10.4169/amer.math.monthly.120.07.660. S2CID 24405635.
Sloane, N. J. A. (ed.). "Decimal expansion of the real part of i!", Sequence A212877; and "Decimal expansion of the negated imaginary part of i!", Sequence A212878. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Decimal expansion of the absolute value of i!", Sequence A212879; and "Decimal expansion of the negated argument of i!", Sequence A212880. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

semanticscholar.org

api.semanticscholar.org

Ivan, M.; Thornber, N.; Kouba, O.; Constales, D. (2013). "Arggh! Eye factorial . . . Arg(i!)". American Mathematical Monthly. 120: 662–665. doi:10.4169/amer.math.monthly.120.07.660. S2CID 24405635.
Sloane, N. J. A. (ed.). "Decimal expansion of the real part of i!", Sequence A212877; and "Decimal expansion of the negated imaginary part of i!", Sequence A212878. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

utoronto.ca

math.utoronto.ca

"What is the square root of $i$ ?". University of Toronto Mathematics Network. Retrieved 26 March 2007.

worldcat.org

Zill, Dennis G.; Shanahan, Patrick D. (2003). A first course in complex analysis with applications. Boston: Jones and Bartlett. pp. 24–25. ISBN 0-7637-1437-2. OCLC 50495529.
Gbur, Greg (2011). Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. pp. 278–284. ISBN 978-0-511-91510-9. OCLC 704518582.

search.worldcat.org

Zill, Dennis G.; Shanahan, Patrick D. (2003). A first course in complex analysis with applications. Boston: Jones and Bartlett. pp. 24–25. ISBN 0-7637-1437-2. OCLC 50495529.
Gbur, Greg (2011). Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. pp. 278–284. ISBN 978-0-511-91510-9. OCLC 704518582.