The Ancient Trick to Measure Earth
55sReveals a mind-blowing ancient technique that sparks curiosity and wonder.
▶ Play ClipAI Summary
This video explains how the ancient Greek scholar Eratosthenes measured the circumference of the Earth using a well, a stick, and geometry. It walks through the key steps of his reasoning, from observing the sun's reflection in a well to calculating the angle and applying a ratio.
Chapters
[00:01]
The Well in Syene
Eratosthenes learned about a well in Syene, Egypt, where on the summer solstice the sun's reflection could be seen at the bottom.
[00:27]
Observation in Alexandria
He waited for the summer solstice and checked his own well in Alexandria, but there was no reflection, indicating the sun was not directly overhead.
[00:42]
Parallel Rays
The sun's rays are effectively parallel because the sun is far away, which is key to the geometric reasoning.
[01:08]
The Tropic of Cancer
On the summer solstice, the Earth's axis is tilted toward the sun, creating a line of latitude where the sun is directly overhead—the Tropic of Cancer.
[01:37]
Measuring the Angle
Eratosthenes measured the angle between the sun's rays and the vertical in Alexandria as about 7 degrees, which corresponds to the arc between Alexandria and Syene.
[01:53]
Calculating the Earth's Size
By taking the ratio of the angle (7°) to 360°, he could deduce the Earth's circumference from the known distance between the two cities.
Mentioned in this Video
Tutorial Checklist
1
00:14
Find a location on the Tropic of Cancer where the sun is directly overhead on the summer solstice.
2
00:27
At noon on the summer solstice, measure the angle of the sun's rays from vertical in your location.
3
00:42
Assume the sun's rays are parallel and that the angle measured corresponds to the arc between your location and the Tropic of Cancer.
5
01:53
Multiply the known distance between the two locations by the ratio to find the Earth's circumference.
Study Flashcards (4)
What phenomenon did Eratosthenes observe in a well in Syene?
easy
Click to reveal answer
What phenomenon did Eratosthenes observe in a well in Syene?
easy
Click to reveal answer
On the summer solstice, the sun's reflection could be seen at the bottom of a well in Syene, Egypt.
00:14
What is the line of latitude where the sun is directly overhead on the summer solstice?
easy
Click to reveal answer
What is the line of latitude where the sun is directly overhead on the summer solstice?
easy
Click to reveal answer
The Tropic of Cancer.
01:24
What angle did Eratosthenes measure between Alexandria and Syene?
medium
Click to reveal answer
What angle did Eratosthenes measure between Alexandria and Syene?
medium
Click to reveal answer
About 7 degrees.
01:37
How did Eratosthenes calculate the Earth's circumference?
hard
Click to reveal answer
How did Eratosthenes calculate the Earth's circumference?
hard
Click to reveal answer
He used the ratio of the angle (7°) to 360° to find the fraction of the Earth's circumference between the two cities, then multiplied the known distance by that fraction.
01:53
💡 Key Takeaways
📊
The Well in Syene
This is the key observation that sparked Eratosthenes' measurement.
00:14
⚖️
Parallel Rays Assumption
Understanding that the sun's rays are parallel is crucial for the geometric reasoning.
00:42
💡
The Tropic of Cancer
This line of latitude is the basis for the measurement.
01:24
🔧
Ratio Calculation
The simple ratio method allowed Eratosthenes to estimate the Earth's size.
01:53Full Transcript
[00:01] learned about you know the technique for measuring the radius of the Earth I think I saw so there's this old TV series called Cosmos and uh the way the story goes is that he had read somewhere of this well in this town called sinin
[00:14] in Egypt uh where on one day of the year the summer soltice you could look down in the well and you could see the sun reflected in the water underneath and he said oh that's kind of cool uh um I don't live there but I have a well in my
[00:27] the same thing so he wait until the summer solstice and he at noon he went down and looked at the well and there was no reflection of the Sun and he knew round let's think of the Sun as far enough away from Earth that all of its
[00:42] rays of light are effectively parallel at any given moment if you draw a line from the center of the earth straight to the sun it passes through some point on the surface which must be experiencing this phenomenon where the sun is
[00:54] directly overhead but if you were someone in aatosan time it would be very difficult to know exactly where this was happening at a given moment so what makes the summer solstice special is that on that day the axis of Earth's
[01:08] rotation is tilted directly towards the Sun and as a result on this day as the Earth revolves around that axis over 24 hours there's a consistent line of latitude where all of the locations on this line predictably experience this
[01:24] phenomenon this line has a special name it's called the Tropic of Cancer and the town cine that aatosan had read about sits on this line now aatosan himself was in Alexandria which is a bit north of that so the direction that he
[01:37] perceives as straight up is going to sit at a certain angle away from the Rays of that Sun so by measuring that this angle was about 7° he could reason that the arc along the planet Earth between his Town Alexandria and Cen is about 7° so
[01:53] if you take the ratio between this angle and the full 360° around a circle that should be the ratio of the distance between his town and Cen and the full know that distance you can deduce the size of the Earth
