Extension of internal ratio of a line segment into complex values and its application to the generalization of Menelaus’ theorem

DOI

10.2991/assehr.k.210508.035How to use a DOI?

Keywords

Line segment, Menelaus’ theorem

Abstract

In mathematics and mathematics education, ranges of application are sometimes generalized. This article studies the generalization of the concept on internally dividing points. The ratios of internally dividing points are usually considered in real numbers since the real numbers are naturally corresponding to the length of line segments. The aim of this article is to extend the range of such ratios into the complex numbers. After defining the complex-valued ratio, we shall apply it to the generalization of Menelaus’ theorem which is famous in elementary geometry.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Masayuki Ichikawa
AU  - Naoyasu Kita
AU  - Hiroto Matsumoto
AU  - Yoshihisa Nakamura
PY  - 2021
DA  - 2021/05/11
TI  - Extension of internal ratio of a line segment into complex values and its application to the generalization of Menelaus’ theorem
BT  - Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
PB  - Atlantis Press
SP  - 9
EP  - 14
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.210508.035
DO  - 10.2991/assehr.k.210508.035
ID  - Ichikawa2021
ER  -