Minimum distance between any two arbitrary points on a sphere or globe given the latitudes & longitudes using vectors

Here is the derivation of an analytic formula using vectors to calculates the minimum distance or great circle distance between any two arbitrary points on the sphere of a finite radius. This formula is extremely useful to calculate the geographical distance between any two points on the globe for the given latitudes & longitudes. This is a highly precision formula which gives the correct values. More
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He is studying for a Master's degree in Production Engineering at Indian Institute of Technology Delhi. He did B. Tech.(Hons) in Mechanical Engineering from Madan Mohan Malaviya University of Technology (Formerly M.M.M. Engineering College), Gorakhpur (UP) India. He did his high school from D.A.V. Inter College, Mahoba (UP) & Intermediate from Oxford Model Inter College, Syam Nagar, Kanpur (UP) India. He made his best efforts more than two years for this academic research in Applied Physics based on mathematical derivations & formulations. He derived a formula on permutations of alphabetic words, positive integral numbers & all other linear permutations,. It had been certified by International Journal of Mathematics & Physical Sciences Research. Manuscript ID: 004022014A. Consequently, he, using his formula, proved that factorial of any natural number can be expanded as the sum of finite terms. This expansion named as 'HCR's Series'
He had been taught, guided & inspired by his renowned & well experienced teacher of Physics Mr Upendra Sir @ Oxford Model I. C. Kanpur. He derived a formula for all five platonic solids which is the simplest & the most versatile formula to calculate all the importamt parameters of regular polyhedra. He worked to analyse Goldberg polyhedra, Archimedean solids & truncated & expanded polyhedra using his Theory of Polygon & his formula for platonic solids.

He wrote his first book Advanced Geometry based on research articles in Applied Mathematics & Radiometry for higher education which was first published by Notion Press, Chennai, India. He also authored a new book 'Electro-Magnetism' in Theoretical Physics which was published with Notion Press in 2020.
Published Papers of the author by International Journals of Mathematics
“HCR’s Rank or Series Formula” IJMPSR March-April, 2014
“HCR’s Series (Divergence)” IOSR March-April, 2014
“HCR’s Infinite-series (Convergence)” IJMPSR Oct, 2014
“HCR’s Theory of Polygon” IJMPSR Oct, 2014

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