A blind spot in undergraduate mathematics: The circular definition of the length of the circle, and how it can be turned into an enlightening example
DOI:
https://doi.org/10.21100/msor.v20i3.1300Keywords:
calculus, engineering mathematics, definition, integral, arc lengthAbstract
We highlight the fact that in undergraduate calculus, the number pi is defined via the length of the circle, the length of the circle is defined as a certain value of an inverse trigonometric function, and this value is defined via pi, thus forming a circular definition. We present a way in which this error can be rectified. We explain that this error is instructive and can be used as an enlightening topic for discussing different approaches to mathematics with undergraduate students.References
Allenby, R., 1997. Numbers and proofs. Elsevier.
Landau, E., 1951. Differential and integral calculus. Chelsea Publishing Company.
Remmert, Reinhold, 2012. "Ch. 5 What is π?". In Heinz-Dieter Ebbinghaus; Hans Hermes; Friedrich Hirzebruch; Max Koecher; Klaus Mainzer; Jürgen Neukirch; Alexander Prestel; Reinhold Remmert (eds.). Numbers. Springer.
Sullivan, M. and Miranda, K., 2014. Calculus: Early Transcendentals. Macmillan Learning.
Thomas, G.B., Finney, R.L., Weir, M.D. and Giordano, F.R., 2003. Thomas' Calculus. Addison-Wesley.
Varberg, D., Purcell, E. and Rigdon, S. E., 2007. Calculus. Pearson Prentice Hall.
Downloads
Published
2022-08-29
Issue
Section
Articles
