Work

Unveiling Janous's Conjecture: Calculus, Algebraic, and Computational Approaches

Year: 2025

Type: article

Abstract: We give a proof of Janous's conjecture: 2 < \frac{\sin A}{A} + \frac{\sin B}{B} + \frac{\sin C}{C} \leq \frac{9\sqrt{3}}{2\pi}, where A, B, C > 0 and A + B + C = \pi which combines integral calculus, geometric optimization, symmetry arguments, supplemented by computational techniques. We also provide an algebraic proof avoiding calculus.

Source: International journal of mathematics and computer science

DOI: 10.69793/ijmcs/02.2025/amara

Authors: Amara Chandoul, Abdallah Assiry

Institutions: University of Sfax, Umm al-Qura University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Umm Al-Qura University

OpenAlex ID: W4409234530

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