The Prytz connections
Geir Bogfjellmo, Charles Curry, Sylvie Vega-Molino

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.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Mathematics and Applications · Algebraic and Geometric Analysis
