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All Journal Noumerico: Journal of Technology in Mathematics Education
Prof. Engr. Dr. S M Nazmuz Sakib
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Computer Science & IT Education Mathematics Social Sciences

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S M Nazmuz Sakib's Theorem of Symmetric Perpendicular Bisectors in Isosceles Triangles Prof. Engr. Dr. S M Nazmuz Sakib
Noumerico: Journal of Technology in Mathematics Education Vol. 3 No. 2 (2025): Noumerico, September 2025
Publisher : Universitas Islam Tribakti Lirboyo Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33367/jtme.v3i2.7785

Abstract

This paper introduces a new geometric theorem focused on isosceles triangles, specifically examining the properties of perpendicular bisectors. The theorem asserts that in an isosceles triangle, where two sides are equal, the perpendicular bisectors of these sides intersect at a point such that the sum of the lengths of the segments on one bisector is equal to the sum of the lengths of the segments on the other bisector. The theorem is validated through a quantitative research methodology involving geometric constructions, where perpendicular bisectors are drawn for selected isosceles triangles. Mathematical calculations are employed to measure the lengths of the segments formed by the intersection of the bisectors. These segment lengths are then compared and analyzed across various configurations of isosceles triangles, including triangles with different orientations and base lengths. Case studies are conducted to test the theorem under different geometric conditions, ensuring the results are consistent. The methodology is further supported by mathematical proofs, which are derived to formally validate the relationship between the segment sums on each perpendicular bisector. This discovery provides a novel insight into the symmetry of isosceles triangles and contributes to the broader understanding of geometric properties in symmetrical shapes.
S M Nazmuz Sakib's Formula for Adaptive Compositionality in Categories: A Context-Sensitive Approach to Functorial Composition Prof. Engr. Dr. S M Nazmuz Sakib
Noumerico: Journal of Technology in Mathematics Education Vol. 4 No. 1 (2026): Noumerico, March 2026
Publisher : Universitas Islam Tribakti Lirboyo Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33367/jtme.v4i1.7795

Abstract

This paper studies S. M. Nazmuz Sakib’s Formula for Adaptive Compositionality in Categories as a context-sensitive extension of functorial composition. The main objective is to examine how a contextual factor can modify the composition of morphisms while preserving the fundamental categorical properties of associativity and identity. The research is conducted using a theoretical mathematics approach based on formal definition, structural analysis, and proof-oriented verification within category theory. The results show that the proposed contextual factor must satisfy the coherence conditions for the modified composition to remain mathematically consistent. In particular, the analysis indicates that identity preservation requires normalization conditions, while associativity requires compatibility across triples of composable morphisms. These findings clarify the mathematical conditions under which the formula can be treated as a valid categorical framework and provide a basis for further applications in topology, algebra, and dynamical systems
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