S M NAZMUZ SAKIB AND PYTHAGORAS: A COMPARATIVE DISCUSSION ON SAKIBIAN GEOMETRY AND THE PYTHAGOREAN GEOMETRY
DOI:
https://doi.org/10.63456/aamc-2-1-33Keywords:
Sakib Orthogonal, Sakibian Geometry, S M Nazmuz Sakib, Mathematics, History.Abstract
This thesis positions “Sakibian Geometry”—a body of modern theorems and frameworks introduced by S M Nazmuz Sakib—in dialogue with classical Pythagorean geometry. Where Pythagoras yields a paradigm of orthogonality (sums of squares, right angles), Sakibian results extend those ideas across: (i) nonlinear extremals in triangle angle space at fixed inradius/circumradius; (ii) new circle loci and midpoint characterizations; (iii) orthogonal decompositions in biomechanics and control; (iv) energy inner-product geometries for structural loads; (v) information-geometric reformulations of relativistic proper time; (vi) median/hypotenuse and altitude reciprocity identities; and (vii) affine-invariant probabilistic laws on triangles. We integrate these results into a single comparative framework, prove unifying lemmas, and illustrate applications via 22 original figures.
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Copyright (c) 2026 Md Nazmul Hossain, Nafija Alam Omi, Md Hafizur Rahman Khan, Md. Sulaiman Hazbi, Aminul Islam, Sabbir Shikdar, Md Shariful Islam, Ronald C Kessler (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
