Integrability of Newton ovals, computation of air damper inlets

TL;DR

This paper explores the algebraic integrability of Newton ovals, clarifies historical mathematical results, and demonstrates an unexpected application in computing air damper inlets, linking pure mathematics with industrial technology.

Contribution

It provides new insights into the algebraic integrability of Newton ovals and connects these mathematical concepts to practical applications in engineering.

Findings

Clarified Newton's results on oval integrability

Linked algebraic geometry to air damper section computation

Highlighted historical mathematical discussions

Abstract

About global and local algebraic integrability of ovals. A contribution to clarify Newton results and relative comments on his work done by Arnol'd and Pourciau. A possibile application to air damper sections computation is offered, as example of unexpected link between pure mathematics and industrial technology.