S M NAZMUZ SAKIB AND PYTHAGORAS: FROM PYTHAGOREAN GEOMETRY TO SAKIBIAN GEOMETRY
Keywords:
Sakibian Geometry, Pythagorean geometry, paradigm of orthogonalityAbstract
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) affineinvariant probabilistic laws on triangles. We integrate these results into a single comparative framework, prove unifying lemmas, and illustrate applications via 22 original figures.
References
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