The Prytz connections

TL;DR

This paper provides a mathematical analysis of the Prytz planimeter using sub-Riemannian geometry and differential geometric concepts like connections and horizontal lifts.

Contribution

It introduces a novel geometric framework for understanding the Prytz planimeter through advanced differential geometry techniques.

Findings

Mathematical description of the Prytz planimeter in sub-Riemannian terms

Analysis of the planimeter using connections and horizontal lifts

New insights into the geometric structure underlying the device

Abstract

The Prytz planimeter is a simple mechanical device that historically was used to approximate areas of plane regions. In this article, we present a mathematical description and analysis of the planimeter in terms of sub-Riemannian geometry and in terms of connections and horizontal lifts -- central concepts in differential geometry.