How Eratosthenes calculated the Earth's circumference
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
🌍 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
💡Satellites
💡Eratosthenes
💡Stick and Shadow
💡Summer Solstice
💡Spherical Earth
💡Cen
💡Stadia
💡Proportions
💡Geometry
💡Pythagoras
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.
Transcripts
[Music]
in the mid 20th century we began
launching satellites into space that
would help us determine the exact
circumference of the earth 40,3
km but over 2,000 years earlier in
ancient Greece a man arrived at nearly
that exact same figure by putting a
stick in the
ground that man was aatosan a Greek
mathematician in the head of the Library
of Alexandria ostanes had heard that in
Cen a city to the south of Alexandria no
vertical Shadows were cast at noon on
the summer solstice the sun was directly
overhead he wondered if this were also
true in Alexandria so on June 21st he
planted a stick vertically in the ground
and waited to see if a shadow would be
cast at noon it turns out there was one
and it measured about
7° now if the sun's rays are coming in
at the same angle at the same time of
day and a stick in Alexandria is casting
a shadow while a stick in Zen is not it
must mean that the earth's surface is
curved and aanes probably already knew
that the idea of a spherical Earth was
floated by Pythagoras around 500 BC and
validated by Aristotle a couple
centuries later if the Earth really was
a sphere aatosan could use his
observations to estimate the
circumference of the entire planet since
the difference in Shadow length is 7°
between Alexandria and Cen that means
the two cities are 7° apart on Earth's
360° surface
ostanes hired a man to Pace the distance
between the two cities and learn there
were 5,000 stadia apart which is about
800 km he could then use Simple
proportions to find the Earth's
circumference 7.2 de is 150th of
360° so 800 km * 50 equals 40,000 km and
just like that a man 2200 years ago
found the circumference of the entire
planet with just a stick and his brain
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