The strength of bones and muscles is proportional to their cross sectional area while their weight is proportional to their volume. As an object (like a leg) gets larger, its strength will increase proportional to the width squared, but the weight will increase proportional to the width cubed.

1. In order to survive, an animal must be able to support its own weight. If we assume that a gorilla can support double its own weight, how large is the largest possible gorilla?
2. Could King Kong exist? What about Godzilla?
3. Why is being big a good strategy for a Sumo wrestler?

Over the past hundred years, better nutrition has resulted in an increase in average height. What is a reasonable upper limit to the height of a human being (assuming body proportions stay about what they are now)? Is there a theoretical limit to how large a land animal can be? What is a good shape for a huge animal (if their only problem is their size)? Is there an optimal shape?

Communicated by A. Johnson.