1.pngIn 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。2.pngBut 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。3.pngSo, 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。