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Reflections on Chinese Numeration Systems: References and About the Author

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

 

References

Beery, Janet, Gary Cochell, Connie Dolezal, Angi Sauk, and Linda Shuey. 2004. Negative Numbers. In Historical Modules for the Teaching and Learning of Mathematics (CD), edited by Victor J. Katz and Karen Dee Michalowicz, 34–44. Washington, DC: Mathematical Association of America.

Dauben, Joseph W., ed. 2007. Chinese Mathematics. In The Mathematics of Egypt, Mesopotamia, China, and Islam: A Sourcebook, edited by Victor Katz, 187–384. Princeton and Oxford: Princeton University Press.

Flagg, Mary. 2017. Solving a System of Linear Equations Using Ancient Chinese Methods. Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS): Linear Algebra. https://digitalcommons.ursinus.edu/triumphs_linear/1.

Grcar, Joseph F. 2011, June/July. Mathematicians of Gaussian Elimination. Notices of the AMS 58(6): 782–792.

Hart, Roger. 2011. Chinese Roots of Linear Algebra. Baltimore: Johns Hopkins University Press.

Lam Lay-Yong and Ang Tian Se. 2004. Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China. Rev. ed. Singapore: Scientific Press.

Needham, Joseph et al. 1954–present. Science and Civilization in China. 7 vol. Cambridge: Cambridge University Press.

Schwartz, Randy K. 2018, December. A Classic from China: The Nine Chapters. Convergence. DOI:10.4169/convergence20181231.

Sigler, Laurence E., trans. 2002. Fibonacci’s Liber Abaci. Berlin: Springer-Verlag.

Siu Man-Keung. 2000. An Excursion in Ancient Chinese Mathematics. In Using History to Teach Mathematics: An International Perspective, edited by Victor Katz, 159–166. Washington, DC: Mathematical Association of America.

Straffin, Jr., Philip D. 1998, June. Liu Hui and the First Golden Age of Chinese Mathematics. Mathematics Magazine 71(3): 163–181.

Suzuki, Jeff. 2020. Chinese Rod Numerals. https://www.youtube.com/watch?v=RnZhwHESI2U.

Swetz, Frank J. 1979, January. The Evolution of Mathematics in Ancient China. Mathematics Magazine 52(1): 10–19. DOI: 10.1080/0025570X.1979.11976742.

Swetz, Frank J. 1987. Capitalism and Arithmetic: The New Math of the 15th Century. Chicago: Open Court Publishing.

Volkov, Alexei. 2018. Chinese Counting Rods: Their History, Arithmetic Operations, and Didactic Repercussions. In Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators, edited by Alexei Volkov and Viktor Freiman, 137–188. Springer Nature Switzerland.

Xu Yibao. 2005, September 10. Review of Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China, by Lam Lay-Yong and Ang Tian Se. MAA Reviews, https://www.maa.org/press/maa-reviews/fleeting-footsteps-tracing-the-conception-of-arithmetic-and-algebra-in-ancient-china-revised-edition.

About the Author

For more than five decades, Frank J. Swetz has advocated for the use of history and culture to enliven and deepen the study of mathematics. In particular, he has described how mathematical developments in non-Western societies might be incorporated into the training of secondary school teachers. His books include Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China (The Penn State Press, 1977); From Five Fingers to Infinity: A Journey Through the History of Mathematics (Open Court Publishing, 1994); and Mathematical Expeditions: Exploring Word Problems Across the Ages (Johns Hopkins University Press, 2012).

Frank J. Swetz (The Pennsylvania State University), "Reflections on Chinese Numeration Systems: References and About the Author," Convergence (February 2022)