Using Monotone Sequence of Functions to Determine the Shortest Arc Length of Circles Connected Any Two Points on Sphere
Muhammad Kabil Djafar (a*), Laode Safiuddin (b), Azwar Dandi Saputra (a)

a). Mathematical Department, Faculty of Mathematics and Natural Sciences, Halu Oleo University, Kendari, 92321, Indonesia
*) muh.kabiljafar[at]uho.ac.id
b). Department of Physical Education, Faculty of Teaching and Educational Science, Halu Oleo University, Kendari, 92321, Indonesia

Abstract

This paper discusses about arc length of circles that connected any two points on sphere. There are infinitely many of circles that connected any two points on sphere. Using monotone sequence of functions, we can show that the shortest arc length of circle that connected any two points on sphere is the circle with the center at the origin.

Keywords: arc length, monotone sequence, bounded sequence

Topic: Educational Aspects of Analysis