A novel proof of the inequality sin x≤x
Year: 2026
Type: article
Abstract: In this paper, a new and insightful proof of the well-known inequality sin x ≤ x , for x ≥ 0 , is presented using some concepts and tools from differential geometry. Unlike standard analytical or calculus-based proofs, this approach draws on geometric intuition and properties of smooth curves, offering a fresh perspective on a classical result. This approach not only provides a rigorous proof, but also enriches the understanding of the inequality by framing it within a broader geometric context, which is accessible to students with a basic knowledge of calculus.
Source: Examples and Counterexamples
Author: Enes Kačapor
Institution: State University of Novi Pazar
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $420
OpenAlex ID: W7135233345