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- Where was Eratosthenes born?(11 votes)
- How did Eratosthenes send message from Syene to Alexandria about the solstice occurring in Syene to measure the shadow of the pole present at Alexandria?(6 votes)
- I think he knew there was no angle at summersolstice, so he only had to measure the length of the shadow at that particular moment at 12 o'clock(6 votes)
- How did Eratosthenes check on his pole at the same time as the other person checked his at noon i.e. how did Eratosthenes know that it was noon at Syene and that he should check his pole's angle?
Is it because of knowing the time of travel from Alexandria to Syene?(4 votes)
- Alexandria and Syene were close enough together (they're both in Egypt) that they used the same time. Essentially, they're in the same time zone. Also Syene is almost directly South of Alexandria meaning that they hit their solar noon (i.e. the actual time when the Sun is directly overhead) just about at the same time.
I've actually lead this experiment with my students before. The important consideration is knowing the time of your local solar noon, which is not necessarily12:00p.m. exactly. On any given day, one point on your longitude (North-South axis) will be directly under the sun at the solar noon: the same position as Syene in the classical problem. If you measure your distance to that point, and measure your shadow at the solar noon, you can calculate the circumference of the earth. Of course, today we have modern tools that can tell you all this information, but it's not impossible to conceive how Eratosthenes gathered this information more slowly and scheduled his measurements at the right time in his age.(3 votes)
- Ok that gives us circumference using that equation based on assumptions. . but where can we do a hard and fast scientific experiment and actually measure the curvature. . and can I assume that the rate would be close to. . 1 mile=8 inches ×the number of miles squared? And if that is correct could you please put it into equation form. . and I'm getting nothing but straight and flat with a telescope at over 100 miles. . so how and where could I do it that would show that ratio of curvature(3 votes)
- Hi thanks for the information.
I have a question I was wondering if you could help me on. It seems this whole calculation is dependent on the assumption that the sun rays are arriving to Earth in a parallel manner. At the time of Eratosthenes what proof is there that this was correct? Cheers.(1 vote)
- 24,901.55/360 =69.1709722 x 16.39721 = 1134.21095
pi x 360 = 1131.408/69 = 16.39721
16.39721 x 22.00 = 352 + 8 = 360
intercalculate from a few decimals and same numbers occur
3.1428 X 360 = 1131.408
24,901.55/1131.408 =22.009345877(4 votes)
- But how can someone not living on the equator measure the circumference ??(1 vote)
- Neither syene nor alexandria are on the equator. Being on the equator or not is irrelevant information.(3 votes)
- How far is it from Alexandria to Syene, the two cities mentioned in the video(1 vote)
- If the circumference wasnt known till modern day, how would they figure it out?(1 vote)
- You mean, other than the method just described in this video?
Eratosthenes used this method to calculate the circumference of the Earth, a method that assumed the Earth is Spherical and used the mathematical properties of spheres and circles with basic angle math to calculate the circumference of the Earth, much like you can calculate the circumference of any circle.
Modern day tools have refined our measurement of the Earth's circumference and allowed us to confirm/compare with Eratosthenes result.(2 votes)
- Can a city with different latitude where the angle is measured be at a different longitude? If it is at different longitude, can we just measure the vertical distance between the corresponding latitudes and measure angles at the local noon time for this method to work?(1 vote)
- Were there any smaller units of stade? Like today, Meter is cm , and that is mm(1 vote)
[MUSIC PLAYING] In this video, we're going to talk about Eratosthenes, who was a Greek scholar that lived about 2,000 years ago. Eratosthenes found a way, using none of the modern tools that we have, to measure the circumference of the Earth. And in this video, we're going to see how he did this. So the heart of Eratosthenes's measurement is a simple geometry problem. So consider the circle shown here, which has points A and B. And let's say that we know the distance that A and B make on the circumference of the circle. So we know the measure of arc AB. Now, the question is, with this knowledge, can we determine the circumference of our circle? And I'm sure you all are thinking that the answer is obviously no because A and B are just two random points on the circle. So just knowing their distance doesn't help us very much. What we need is some information that makes A and B not just random points on the circle anymore. We need to know the angle that A and B make with the center of the circle. Once we know this, we know how far around A and B go on the circle because we know that every circle has in it 360 degrees in one full revolution. So by knowing theta, we know the fraction of the circle that the arc AB takes up, and we can simply extrapolate to find the circumference. So let's make this one a little clearer with some concrete examples. So let's look at the circle on the right now. And again, we have points A and B. And here you can clearly see that the angle that A and B make with the center of the circle is 90 degrees. And since we know that 90 goes into 360 four times, arc AB is 1/4 around the circle, meaning that the piece shown here, the shaded piece, will fit into the circle four times. So in this case, the circumference of the circle is four times the length of arc AB. Now let's just drive the point home further with this other circle. Again, we have points A and B. And here the angle between points A and B, let's say we measure, and it turns out to be 36 degrees. So since 36 goes into 360 ten times, we know that 10 of these pieces will fit into the circle. And in this case, the circumference is 10, which is the number of pieces, times the length of one piece, AB. Now, in general, the circumference of the circle is given by the number of pieces we have times the length of one piece. And just right inside explicitly, the number of pieces is 360 degrees divided by theta, the angle that A and B make with the center of the circle. And the length of one piece is simply AB. So now, if we just know these two things, the arc AB and the angle A and B make with the center of the circle, we can determine the circumference. And this is really the heart of Eratosthenes's method. So now let's apply this. Now we have another circle, but this time we'll explicitly identify the circle as the Earth, and point A becomes a city, Alexandria. This is a city in Egypt, and this is where Eratosthenes lived. Point B now becomes the city of Syene. So in Eratosthenes's day, it was known that the distance between Alexandria and Syene was about 500 miles. Of course, back then the units weren't miles. But we know the conversion factor, so we don't have to worry about the old system of units. The distance between Alexandria and Syene is 500 miles. And now, looking back at our previous problem, we see that all we have to do to figure out the circumference of the Earth given this information is to figure out the angle that Alexandria and Syene make with the center of the Earth. And the really brilliant thing about Eratosthenes's method is that he found a nice way to measure this angle. So how did he do this? It was known that in Syene there was a well, a long, deep well such that at noon on the summer solstice you could see the sun's rays light up in the bottom of the well. And if you think about this, what this means is that since this well is such a deep thing, this means that the sun's rays must have been coming into the Earth parallel to the well. So we draw these rays, and we see the sun is very, very far away from the Earth. And because the sun is so far away, we can treat the rays coming in from the sun at different points as parallel. So here we've drawn the ray that comes in at Alexandria and the ray at Syene. Now, it's an interesting property of parallel lines that if we have these two parallel lines shown here, the two rays, and we have the radii also shown, this angle that we've called theta 2 is equal to the angle that we're trying to find, theta 1. This is a fact that you might have been exposed to in your geometry classes. It's called the property of corresponding angles. But regardless, it's pretty easy to prove to yourself. So since we know this, now we can transform the hard problem of measuring theta 1 to the relatively easier problem of measuring theta 2. So how do we measure theta 2? It's pretty straightforward. So let's zoom in on this region. We have the surface of the Earth as one of the important lines. And then the radius gets translated into a vertical stick. And we also have the sun with one of its rays. So this ray casts a shadow on the ground. And by knowing the length of the shadow and the height of our stick, we can construct this triangle and simply measure the angle theta 2. All we have to do is look at the shadow created off of a stick. And this is exactly what Eratosthenes did. And he measured that the angle theta 2 was equal to 7.2 degrees. So now we have this information. The angle theta, which is called theta now, is equal to 7.2 degrees. And the measure of the arc AB, or Alexandria to Syene, is 500 miles. So with this information, now all we have to do is feed this into the formula that we got earlier. Let's just recall it-- C equals 360 degrees divided by theta times AB. And so this is very simple to do. We plug in 7.2 degrees for theta. We plug in 500 miles for AB. And in the end, we find that C is equal to 50 times 500 miles, or 25,000 miles. So this is our estimate, or Eratosthenes's estimate, for the circumference of the Earth. Let's call that C Eratosthenes. And so see how simple it was for us to get this. But notice that, according to our modern measurements, the average circumference of the Earth, because it's not a perfect sphere, is around 24,900 miles. So we were only about 100 miles off with this seemingly primitive method, which is about half a percent off. So this is a very impressive thing for someone who lived so long ago without the access to these tools that we now use. [MUSIC PLAYING]