H. Rajpoot's cosine formula to compute the angle between the chords of any two great circle arcs meeting at a common end point at some angle (Geometry of Sphere)

H. Rajpoot's cosine formula is a dimensionless formula which is independent of radius of the sphere & holds equally good for all the spherical surfaces to compute the angle between the chords of any two great arcs meeting or intersecting each other at a common end point at some angle. It is used to find out the minimum distance between any two points on any sphere of finite radius. More
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About HARISH CHANDRA RAJPOOT

Harish Chandra Rajpoot is B. Tech. graduate of 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) India & 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.
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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