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In the mid 20th century, we began launching satellites into space that would help us determine the exact circumference of the Earth: 40,030 km. But over 2000 years earlier, a man in Ancient Greece came up with nearly the exact same figure using just a stick and his brain. Following is a transcript of the video.
20世纪中期，我们开始向太空发射卫星，从而帮助我们确定了地球的精确周长为40,030公里。然而，早在2000年前，古希腊的一个人仅用一根棍子和他的大脑，得到了一个几乎完全相同的数字。以下是该视频的文字记录。
How an ancient Greek mathematician calculated the Earth’s circumference. In the mid 20th century, we began launching satellites into space that would help us determine the exact circumference of the Earth, 40,030 km.
一名古希腊人是如何计算出地球的周长的?20世纪中期我们才开始往太空发射卫星，帮助我们确定了地球的真实周长为40,030公里。
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 Eratosthenes. A Greek mathematician and the head of the library at Alexandria.
但是在两千多年前的古希腊已经有一个人仅用一根棍子和他的大脑，得到了一个几乎完全相同的数字。这个人就是埃拉托色尼，古希腊的一位数学家、亚历山大里亚图书馆的馆长。
Eratosthenes had heard that in Syene, a city 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.
埃拉托色尼曾听说，在亚历山大港南部的赛尼城，夏至那天正午时垂直的物体没有出现影子，太阳直射在头顶上。他思考着在亚历山大港是否也是如此。
So, on June 21 he planted a stick directly 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 degrees.
因此，在6月21日夏至那天，他把一根棍子垂直插在地上，等着看在正午时会不会出现影子。结果发现有影子，测量发现太阳光线与地面的角度为7度。
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 Syene is not, it must mean that the Earth’s surface is curved. And Eratosthenes probably already knew that.
那么，如果太阳光线在一天的同一时间以同样的角度照射进来，亚历山大港的一根棍子在地上投射出了影子，赛尼城的却没有影子，那么它一定意味着地球的表面是弯曲的。因此，埃拉托色尼很可能已经知道地球是圆球体。
The idea of a spherical Earth was floated around by Pythagoras around 500 BC and validated by Aristotle a couple centuries later. If the Earth really was a sphere, Eratosthenes could use his observations to estimate the circumference of the entire planet.
毕达哥拉斯在约公元前500年就提出了一个球形地球的概念，并被几个世纪后的亚里士多德证实。如果地球真的是一个球体，埃拉托色尼可以用他的观测来估计整个地球的周长。
Since the difference in shadow length is 7 degrees in Alexandria and Syene, that means the two cities are 7 degrees apart on Earth’s 360 degrees surface. Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 kilometers.
由于亚历山大港和赛尼城的阴影长度的差异是7度，这意味着这两个城市在地球360度的表面上相距7度。于是埃拉托色尼雇了一个人来测量这两个城市之间的距离，得知两者相距约5000视距尺，大约是800公里。
He could then use simple proportions to find the Earth’s circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers. And just like that, a man 2200 years ago found the circumference of our entire planet with just a stick and his brain.
然后，他使用简单的比例公式计算出了地球的周长——7.2度是360度的50分之1，因此，800乘以50就午到了40000公里。就是这样，2200年前的这个人仅用一根棍子和他的大脑，就知道了地球的周长。
This video was produced by Alex Kuzoian.
该视频由亚历克斯制作。
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