# Some estimates of precision of the Huygens approximation

## TL;DR

This paper analyzes the accuracy of the Huygens approximation for small angles by establishing bounds for the function using polynomial and rational functions.

## Contribution

It provides new bounds and estimates for the precision of the Huygens approximation near zero, enhancing understanding of its accuracy.

## Key findings

- Derived bounds for the Huygens function near zero
- Compared polynomial and rational function approximations
- Quantified the approximation's accuracy in a specific interval

## Abstract

In this paper are given some estimates of precision of the Huygens approximation $x \approx \frac{2}{3} \sin x + \frac{1}{3} \tan x,$ for right neighbourhood of zero, by determining some boundaries for the Huygens function $f(x) = \frac{2}{3} \sin x + \frac{1}{3} \tan x,$ for $x \in \left(0, \frac{\pi}{2} \right)$, in forms of some polynomial and some rational functions.

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Source: https://tomesphere.com/paper/1907.09301