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Journal of Educational Research in Mathematics -
Vol. 31 ,
No. 1

[ Article ] | |

Journal of Educational Research in MathematicsVol. 31, No. 1, pp.1-15 | |

Abbreviation: JERM | |

ISSN: 2288-7733 (Print) 2288-8357 (Online) | |

Print publication date 28 Feb 2021 | |

Received 22 Oct 2020 Revised 05 Feb 2021 Accepted 05 Feb 2021 | |

DOI: https://doi.org/10.29275/jerm.2021.02.31.1.1 | |

Reconsidering Newton’s Intuition Related to the Fundamental Theorem of Calculus | |

Park, SunYong ^{*}
| |

*Professor, Yeungnam University, South Korea (polya@yu.ac.kr) | |

Funding Information ▼ |

Abstract

The purpose of this study is to refute an argument in Kang (2019) and offer alternative views concerning the analysis of the historical genesis of the fundamental theorem of calculus. Kang (2019) indicated that Newton might have gained insight into the fundamental theorem of calculus using the area increments intuition based on strict distinctions of dimensions. In response, this study seeks to show that Newton addressed his method by focusing on the mean and instantaneous rate of area change rather than the area increments as in the analytic geometry characteristic that breaks the principle of homogeneity. The results of this study also show that the area increments intuition remains pertinent to implicitly recognizing the existence of average height.

Keywords: fundamental theorem of calculus, instantaneous ratio of change, intuition, average height, mean ratio of change |

Acknowledgments

이 연구는 2020년도 영남대학교 학술연구조성비에 의한 것임.

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Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).

Submitting manuscripts for peer review as well as other correspondences can either be made via online by an email (ksesm@daum.net) or sending a mail at Secretariat of

Journal of Educational Research in Mathematics, #1305 Daewoo The'O Ville, 115 Hangang-daero, Yongsan-gu, Seoul, 04376, Republic of Korea (Tel: +82‐2‐797‐7780, Fax: +82‐2‐797‐7750).