How Eratosthenes calculated the Earth's circumference

Business Insider

10 Sept 201602:02

Summary

TLDRIn ancient Greece, Eratosthenes, head of the Library of Alexandria, ingeniously calculated Earth's circumference using a stick and observations of shadows during the summer solstice. He noted a 7° difference in shadow angles between Alexandria and Syene, cities 5,000 stadia apart. By assuming Earth's spherical shape, he applied simple proportions, equating 7.2 degrees to 1/50th of 360°, to estimate Earth's circumference at approximately 40,000 km, remarkably close to modern measurements.

Takeaways

🚀 In the mid-20th century, satellites were launched to determine the Earth's circumference, which was found to be approximately 40,000 km.
🏺 Over 2,000 years earlier, the Greek mathematician Eratosthenes estimated the Earth's circumference using a simple experiment.
🌞 Eratosthenes observed that at noon on the summer solstice, a stick in Syene (modern-day Aswan) cast no shadow, indicating the sun was directly overhead.
📍 He also noted that in Alexandria, a stick cast a shadow at noon on the same day, measuring about 7°.
🌐 Understanding the Earth's curvature, Eratosthenes deduced that the difference in shadow angles meant the Earth's surface was curved.
📚 Building on the spherical Earth theory proposed by Pythagoras and validated by Aristotle, Eratosthenes used his observations to calculate the Earth's size.
📏 He had the distance between Alexandria and Syene measured, finding it to be 5,000 stadia (approximately 800 km).
🧮 Eratosthenes applied simple proportions to calculate the Earth's circumference, using the 7° difference and the measured distance.
🌍 He estimated the Earth's circumference to be 40,000 km, remarkably close to the modern value.
🧠 Eratosthenes' method showcased the power of observation, critical thinking, and mathematical reasoning in ancient times.

Q & A

Who was Eratosthenes and what was his role in ancient Greece?
-Eratosthenes was a Greek mathematician and the head of the Library of Alexandria in ancient Greece.
What was the significance of the observation made in Syene during the summer solstice?
-In Syene, no vertical shadows were cast at noon on the summer solstice, indicating the sun was directly overhead.
What did Eratosthenes observe in Alexandria on the same day?
-In Alexandria, Eratosthenes observed a shadow at noon on the summer solstice, which measured about 7°.
How did the difference in shadows between Syene and Alexandria indicate the Earth's curvature?
-The difference in shadows indicated that the Earth's surface is curved, as the sun's rays were coming in at the same angle but creating different shadow lengths in the two locations.
What was the significance of the 7° difference in shadow length observed by Eratosthenes?
-The 7° difference in shadow length meant that the two cities were 7° apart on the Earth's 360° surface.
How did Eratosthenes measure the distance between Alexandria and Syene?
-Eratosthenes hired a man to pace the distance between the two cities, which was found to be 5,000 stadia, or approximately 800 km.
What method did Eratosthenes use to calculate the Earth's circumference?
-Eratosthenes used simple proportions, considering that 7.2° is 1/50th of 360°, and then multiplied the distance between the two cities by 50 to find the Earth's circumference.
What was the estimated circumference of the Earth calculated by Eratosthenes?
-Eratosthenes estimated the Earth's circumference to be approximately 40,000 km.
How did Eratosthenes' method compare to modern satellite measurements?
-Eratosthenes' method of calculating the Earth's circumference was remarkably close to modern satellite measurements, which determine the Earth's circumference to be about 40,075 km.
What earlier theories supported the idea of a spherical Earth before Eratosthenes' calculations?
-The idea of a spherical Earth was proposed by Pythagoras around 500 BC and later validated by Aristotle.

Outlines

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🌍 Calculating Earth's Circumference with a Stick

In the mid-20th century, satellites were launched to determine Earth's circumference, measuring it at 40,300 km. However, over 2,000 years prior, the ancient Greek mathematician Eratosthenes, head of the Library of Alexandria, approximated this figure using a simple experiment. He was aware that in Syene (modern-day Aswan), no vertical shadows were cast at noon on the summer solstice, indicating the sun was directly overhead. In Alexandria, he observed a 7° shadow at the same time. Assuming a spherical Earth, he deduced that the angle difference represented a 7/360 portion of the Earth's circumference. He then had the distance between the two cities measured, finding it to be 5,000 stadia (approximately 800 km). Using this, he calculated the Earth's circumference as 800 km multiplied by 50, resulting in an estimate of 40,000 km, remarkably close to the modern measurement.

Mindmap

Keywords

💡Circumference

Circumference refers to the distance around a closed curve or the length of the boundary of a circle. In the context of the video, it is used to describe the total distance around the Earth. The script narrates how Eratosthenes, using his observations and calculations, was able to estimate the Earth's circumference to be approximately 40,000 km, which is remarkably close to the modern measurement.

💡Satellites

Satellites are artificial objects that have been intentionally placed into orbit around the Earth or other celestial bodies. The script mentions that in the mid-20th century, satellites were launched into space to help determine the Earth's circumference, showcasing the progression from ancient methods to modern technology.

💡Eratosthenes

Eratosthenes was an ancient Greek mathematician and the head of the Library of Alexandria. He is known for his method of calculating the Earth's circumference. The video highlights his innovative approach by using a stick, shadows, and simple geometry to estimate the Earth's size, which was a significant achievement for his time.

💡Stick and Shadow

In the script, Eratosthenes used a simple experiment involving a stick and its shadow to measure the angle of the sun at noon. The presence or absence of a shadow at the same time in different locations indicated the curvature of the Earth. This observation was a key part of his method for calculating the Earth's circumference.

💡Summer Solstice

The summer solstice is the day with the longest period of daylight in the year when the sun is at its highest position in the sky for the longest period of time. In the script, Eratosthenes chose the summer solstice to conduct his experiment because the sun's position would be most directly overhead at noon, providing the clearest shadow for measurement.

💡Spherical Earth

The concept of a spherical Earth is the idea that the Earth is shaped like a sphere. The script mentions that this idea was proposed by Pythagoras and validated by Aristotle. Eratosthenes' experiment further supported this concept by demonstrating the Earth's curvature through the observation of shadows.

💡Cen

Cen, or Syene as it was known in ancient times, is a city located to the south of Alexandria. The script highlights that at noon on the summer solstice, no vertical shadows were cast in Cen, indicating the sun was directly overhead. This fact was crucial for Eratosthenes to calculate the Earth's circumference.

💡Stadia

Stadia was an ancient unit of distance measurement, often used in Greek and Roman times. In the script, the distance between Alexandria and Cen was measured in stadia. The man hired by Eratosthenes found that the two cities were 5,000 stadia apart, which was a key piece of data for Eratosthenes' calculations.

💡Proportions

Proportions refer to the concept of equality in ratios, which is a fundamental principle in mathematics. In the video, Eratosthenes used proportions to calculate the Earth's circumference. By understanding that a 7° difference in shadow angle represented a 150th part of the Earth's 360° surface, he could scale up the measured distance between cities to estimate the total circumference.

💡Geometry

Geometry is a branch of mathematics that deals with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. The script illustrates how Eratosthenes applied geometric principles to his observations of shadows and the sun's position to deduce the Earth's curvature and calculate its size.

💡Pythagoras

Pythagoras was an ancient Greek philosopher and the eponym of the Pythagorean theorem. The script mentions that he was one of the early proponents of the idea of a spherical Earth, which was later empirically tested and supported by Eratosthenes' calculations.

Highlights

In the mid-20th century, satellites were launched to determine Earth's circumference.

Ancient Greek mathematician Eratosthenes estimated Earth's circumference over 2,000 years ago.

Eratosthenes used a simple method involving a stick and observations of shadows.

In Syene, no vertical shadows were cast at noon on the summer solstice.

In Alexandria, a 7° shadow was observed at the same time, indicating a curved Earth's surface.

The spherical Earth theory was proposed by Pythagoras around 500 BC.

Aristotle later validated the spherical Earth concept.

Eratosthenes calculated the Earth's curvature by comparing shadows in two cities.

The 7° difference in shadow length meant the cities were 7° apart on Earth's 360° surface.

A man paced the distance between Alexandria and Syene, finding it to be 5,000 stadia (about 800 km).

Eratosthenes used simple proportions to estimate Earth's circumference as 40,000 km.

The method involved multiplying the distance between cities by 50 to account for the 7° angle.

Eratosthenes' calculation was remarkably close to the modern value of Earth's circumference.

The ancient method demonstrates the power of observation and simple mathematics.

This historical achievement showcases the ingenuity of early scientists.

Eratosthenes' work predates modern satellite technology by over two millennia.

The stick and shadow method is a testament to the early understanding of Earth's spherical shape.

This ancient calculation method has had a lasting impact on geography and astronomy.