You are here

The Shape and Size of Earth

Dino Boccaletti
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
, on

It is the fiftieth anniversary of the famous color photograph of the earth floating in space taken by Bill Anders of the Apollo 8 crew. That image continues to have the power to astonish. It also reminds us that photographs taken from space gave us our first visual evidence of the earth’s shape. Yet the idea that the earth is round — and even an estimate of its dimensions — has been around at least since the time of Eratosthenes.

It was George Pólya’s enthusiastic appreciation of Eratosthenes that inspired the author’s investigations that led to this book. In Mathematical Methods in Science Pólya wrote, “That Eratosthenes’ result is inaccurate does not really detract from the greatness of his achievement. It is his method that excites our admiration … At Alexandria at noon on a certain midsummer’s day long ago, he observed the shadow cast by a little stick and used his protractor.”

This book traces the history of ideas about the size and shape of the earth from Greco-Roman times to the present. While some of the author’s considerations are scientific and technical, much of his treatment focuses on the cultural and religious influences that shaped common opinions in each historical period. It is more than a little ironic that the same first ten verses of Genesis read by the Apollo astronauts that seemed so fitting at the time of their mission had also been used for several hundred years to condemn the idea that the earth was round.

The author notes that his exploration of twenty-five centuries of thought tells us that the idea that the earth has a spherical shape requires suitable conditions and sufficient time to establish itself as a shared belief. One of the most surprising aspects of the history is that throughout the roughly seven centuries of the Roman republic and empire, the roundness of the earth was never a popular idea and was controversial even among intellectuals. Nor did the Romans, despite the scope of their road building, have any interest in “measuring the world”. They knew the distances between cities connected by their roads, so to them the world might as well have been flat.

Measuring the world — determining the length of a degree of latitude, and thereby estimating the circumference of the world — seems to have begun in the early sixteenth century with the work of Jean Fernel. Fernel combined astronomical observation with calculations of distances using revolutions of the wheels of a stagecoach. In so doing he invented the science of geodesy. Somewhat later Snell (he of “Snell’s Law” in optics) devised a more accurate method of measuring arc length along a meridian using triangulation. French mathematicians and physicists enthusiastically followed up with measurement of the “Meridienne de Paris”.

Newton and Huygens argued that the earth’s shape must be approximately spheroidal, flattened at the poles, because of its rotation. In the modern era, with the benefit of satellites and their sensors, we characterize the earth as a geoid, determined formally as a gravitational equipotential surface that provides a reference for nominal sea level from which heights and depths can be measured. The gravitational positioning system GPS, requiring a spheroidal model on which to specify latitude and longitude, uses a standard reference ellipsoid as an approximation to the geoid.

The author takes the reader through the long development, era by era. He relishes the historical details and offers longish digressions when something catches his interest as well as extension quotations (in Latin) from original sources.

This is a monograph likely to be of most interest to students of intellectual and scientific history. The index unfortunately includes only names of people, so it is difficult to find specific information without an associated name.

Bill Satzer ( was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

See the table of contents in the publisher's webpage.