Ruler and compass constructions in the Lemniscate and the 17-gon

TL;DR

This paper develops ruler and compass constructions within the lemniscate curve, enabling geometric operations like halving and doubling, and details the construction of a regular 17-gon related to lemniscatic points.

Contribution

It introduces practical ruler and compass methods for lemniscate constructions and provides the first detailed construction of the lemnatomic regular 17-gon.

Findings

Methods for halving, doubling, adding, subtracting lemniscate arcs

Construction recipes for lemniscatic geometric operations

Explicit construction of the lemnatomic regular 17-gon

Abstract

We present several ruler and compass practical geometric constructions that can be performed in the lemniscate curve. To be precise, we provide recipes for halving, doubling, adding, subtracting, and transferring lemniscate arcs with ruler and compass. This note complements the instructions for the lemnatomic equilateral triangle and pentagon discussed in \cite{GoLa}, giving the details for the construction of the lemnatomic regular $17$-gon.