The Parallelometer: a mechanical device to study curvature

TL;DR

The paper introduces the Parallelometer, a mechanical device for measuring surface curvature, illustrating parallel transport, Berry phase, and connecting to the Foucault pendulum, with results matching theory and suitable for beginners.

Contribution

It presents a simple, inexpensive mechanical device to study surface curvature and related phenomena, enhancing educational demonstrations.

Findings

Device accurately measures surface curvature

Demonstrates parallel transport and Berry phase

Results align with theoretical predictions

Abstract

A simple mechanical device is introduced, the parallelometer, that can be used to measure curvatures of surfaces. The device can be used as a practical illustration of parallel transport of a vector and to study Berry phase shift when it is carried along a loop on the surface. Its connection to the Foucault pendulum is discussed. The experimental results can be successfully compared with the theoretical expectations. The experiment is inexpensive and conceptually easy to perform and understand for a beginner.