# Some new estimates of precision of Cusa-Huygens and Huygens approximations

## TL;DR

This paper introduces new upper bounds for the Cusa-Huygens and Huygens approximations, using polynomial and rational functions to improve the estimation accuracy of these classical approximations.

## Contribution

The paper provides novel upper bounds for the Cusa-Huygens and Huygens approximations expressed as polynomial and rational functions.

## Key findings

- New polynomial bounds improve approximation accuracy.
- Rational function bounds offer tighter estimates.
- Results enhance understanding of classical approximation methods.

## Abstract

In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.