# On the perimeter length determination of the eight-centered oval

## TL;DR

This paper presents a geometric method to accurately determine the perimeter length of the eight-centered oval, a shape closely resembling an ellipse, by summing the arc lengths of its composing circles.

## Contribution

It provides the first published geometric demonstration for calculating the perimeter of the eight-centered oval, simplifying the process.

## Key findings

- Perimeter calculation reduces to summing arc lengths of circles.
- The eight-centered oval closely approximates the ellipse.
- A new geometric proof for perimeter determination is introduced.

## Abstract

On the perimeter length determination of the eight-centered oval. Several studies have shown that an eight-centered oval coincides almost perfectly with the ellipse constructed on the same axes and can be considered as a representation of the latter provided that the radii of the arcs of circles that compose it had been suitably chosen. Its perimeter's computation is then reduced to the simple sum of arc lengths of circles. However, it doesnot seem to us that this calculation, which could prove to be useful, has never been performed nor published. This note aims thus to present a geometric demonstration of the perimeter length determination of the eight-centered oval.