On the stability of four legged tables

TL;DR

This paper proves that a perfect four-legged square table can be stabilized on irregular ground with limited slope through a small rotation, and discusses extensions to non-square tables and circular foot arrangements.

Contribution

It introduces a mathematical proof demonstrating the stability of four-legged tables on uneven surfaces and explores conditions for equilibrium beyond square tables.

Findings

A perfect square table can be stabilized with less than 90° rotation on ground with up to 15° slope.

The method applies to irregular terrains, ensuring equilibrium.

Conjecture: equilibrium is possible if the four feet lie on a circle.

Abstract

We prove that a perfect four-feet square table, posed in a continuous irregular ground with a local slope of at most 15 degrees can be put in equilibrium on the ground by a "rotation" of less than 90 degrees. We also discuss the case of non-square tables and make the conjecture that equilibrium can be found if the four feet are on a circle