# Explore the Mathematics of the Explorers

## Columbus and other explorers relied upon mathematical calculations using the Earth, stars, and ship speed.

By Donna Iadipaolo

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Christopher Columbus is sometimes a subject of controversy when studied in schools today. However, often absent from any debate is an objective study of the mathematics that Columbus and other explorers of the era relied upon in their pursuits. To start with, Columbus needed to create a proposal for King Ferdinand and Queen Isabella of Spain, which included a calculation of the distance to India. So what were the different estimates of the Earth’s size used to calculate his proposed voyage to India? This is a query students can discover the answers to using a variety of history's attempts.

One early estimate of the Earth's size students could investigate was formulated by the ancient Greek philosopher Aristotle (384-322 BC), who argued that the Earth was spherical because of the circular shadow it cast on the Moon during a lunar eclipse. Then we might turn to the calculation by the Greek mathematician Eratosthenes who estimated the circumference of the Earth to be 250,000 “stadia.” (The stadium, about the size of a sports arena, was a unit of distance used by the Greeks.) Eratosthenes used the idea of the fraction of a circle, that is degrees, and a shadow to arrive at his number. It is also said that al Ma’mun, who ruled Bagdad from 812 to 833, sent out teams of surveyors to measure a north-south baseline and from that measurement obtained the radius of the Earth. Remarkably, these early civilizations came close to arriving at the current measurements of the Earth’s dimensions.

Contrary to popular belief, Columbus was not initially rejected because his opponents believed that the earth was flat. Rather, they believed he underestimated the world’s size. History tells us that Ferdinand’s panel used the original value of the circumference (250,000 stadia by Eratosthenes) to determine the distance to India, and at first rejected Columbus’s proposal as too far a distance to successfully travel. Columbus is said to have underestimated the distance to India, according to some accounts, because he confused the Arab mile (used by al Ma’mun), with the Roman mile (which our own mile is based on). Regardless of the various estimates, measurements, units, and reasoning, in the end, Columbus’s voyage was approved and “in 1492, Columbus sailed the ocean blue.” This month, explore the Earth’s dimensions, horizon measurements, and navigational mathematics elaborated upon in the following math lessons.

## Christopher Columbus, Explorers, and Mathematics:

The Round Earth and Christopher Columbus

Students reflect on various studies of the Earth’s shape and size throughout history. They connect these calculations to Christopher Columbus’s attempt to reach India.

This lesson investigates the methods that the great navigators used to stay on course. The navigational process “dead reckoning” used by Columbus and other navigators of his era is investigated, which uses speed, time, and direction. Also, celestial navigation, using one’s latitude is also discussed.

Students plot constellations on a grid map. They also investigate how explorers planned their travels using constellations as a guide.

Students utilize mathematics to help them build a more complete model of the Earth.