The Block Stacking Problem

The Block Stacking Problem

John D. Norton

Department of History and Philosophy of Science

University of Pittsburgh

https://sites.pitt.edu/~jdnorton/jdnorton.html

February 21, 2025

1. Introduction

In the block stacking problem, a collection of blocks are to be stacked at a table edge. If we stack the blocks so that they protrude past the edge of the table, how far can they go horizontally? The curious and then surprizing result is that we can extend the stack horizontally arbitrarily far. We just need to have a high enough stack of many blocks. Until we think more about it and perhaps do some sums, that just seems wrong. Surely, we expect that there is a limit to how far the stacks can go before the whole stack topples off the edge.

A good general exploration is given by John F. Hall, "Fun with Stacking Blocks" American Journal of Physics, 73, No. 12, December 2005, pp. 1107-16.

There is a long standing literature on the problem that extends back to the mid-19th century. This literature has given the physics in much detail for both the simple case to be dealt with here and for more complicated cases.

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