How Did Eratosthenes Calculate The Circumference Of The Earth

How Did Eratosthenes Calculate The Circumference Of The Earth

In the ancient world, when technological advancements were scarce and the understanding of the Earth’s dimensions was rudimentary, one man’s intellect soared above the rest. Eratosthenes, a Greek polymath of the third century BCE, devised a groundbreaking method to calculate the Earth’s circumference. His ingenious approach, rooted in mathematics and keen observation, remains a testament to human ingenuity and intellectual curiosity.

Eratosthenes’ Quest

Eratosthenes’ journey to measure the Earth’s circumference began with a simple observation. He noticed that during the summer solstice, in the city of Syene (now Aswan, Egypt), vertical objects cast no shadows at noon. This phenomenon sparked his curiosity. He hypothesized that the sun was directly overhead at Syene during the summer solstice, an assumption crucial to his calculations.

The Experiment

Eratosthenes realized that if the sun was directly overhead in Syene on the summer solstice, then at another location where vertical objects cast shadows at noon, the angle of the sun’s rays would differ. He conducted an experiment in Alexandria, Egypt, measuring the angle of the shadow cast by a vertical object at noon on the same day as the summer solstice.

Using basic geometry, Eratosthenes determined the angle of the shadow in Alexandria to be about 7.2 degrees. He knew the distance between Alexandria and Syene to be approximately 800 kilometers, a value he obtained from travelers’ reports and measurements. Armed with these two pieces of information, Eratosthenes set out to calculate the Earth’s circumference.

The Calculation

Eratosthenes understood that if the angle between Syene and Alexandria was 7.2 degrees, it represented 1/50th of a full circle (360 degrees). Therefore, the distance between Syene and Alexandria corresponded to 1/50th of the Earth’s circumference.

By simple proportion, Eratosthenes calculated the Earth’s circumference to be approximately 40,000 kilometers, remarkably close to the modern value of approximately 40,075 kilometers. This astonishing feat of calculation, achieved over two millennia ago, showcases Eratosthenes’ brilliance and the power of human intellect.

Legacy and Significance

Eratosthenes’ method not only provided an accurate estimation of the Earth’s size but also laid the groundwork for future scientific inquiry. His approach demonstrated the importance of observation, measurement, and mathematical reasoning in understanding the natural world.

Moreover, Eratosthenes’ calculation of the Earth’s circumference challenged prevailing beliefs about the planet’s shape and size. His work paved the way for further exploration and scientific advancements, shaping the course of human history.

Eratosthenes’ calculation of the Earth’s circumference stands as a testament to human intellect and curiosity. His ingenious method, rooted in observation and mathematical reasoning, provided a remarkably accurate estimation of the planet’s size over two millennia ago. Today, Eratosthenes’ legacy lives on as a beacon of scientific inquiry and a reminder of the enduring power of human curiosity and ingenuity.