 Now, let's find out how big the Earth is. Using geometry as a key technique, around 200 BC, Aristophanes actually calculated the size of the Earth and came pretty close. Aristophanes used Aristotle's ideas that, one, if the Earth was round, the Sun would appear at different positions to observers at different locations. And two, if the Sun were very far away, the light rays would be almost parallel between any two locations. For his two locations, Aristophanes chose Alexandria and Sain, now Aswan. He knew how far apart these two cities were, 793 kilometers in today's units. Aristophanes knew that on the first day of summer, the Sun passed directly overhead at Sain. At midday, on the same day, using a tower in Alexandria, he measured the angular displacement of the Sun from overhead. He found that the angular displacement was 7.2 degrees. That's approximately one-fiftieth of a circle. Geometry tells us the angle measured at the tower is the same as the angle between lines connecting the two cities to the center of the Earth. This is because when a straight line crosses parallel lines, it crosses them at the same angle. So given that the angle is one-fiftieth of a circle, the distance between the cities will be one-fiftieth of the circumference of the Earth. Thus the circumference can be estimated by multiplying the distance between the two cities by 50, which equals 39,650 kilometers. The actual number at the equator is 40,074 kilometers. So he was only 1% off. This is an experiment anyone can do. In fact, in 2005, it was a science project for a number of schools around the country. I'll point you to details in the credits in case you'd like to try it yourself. Once we have the circumference, geometry gives us the rest. For a spherical Earth, the diameter is equal to the circumference divided by pi, 12,756 kilometers. The radius is half the diameter, so it's 6,378 kilometers. The surface area is 4 times the radius squared times pi. That's 511 million square kilometers. And the volume is 4-thirds the radius cubed times pi. That's 1.07 trillion cubic kilometers. Needless to say, this is very large. A high school teacher calculated the number of students that could fit inside the Earth. It came to 137,188,690 times 10 to the 12th students. This number of students is so large that if you could count one number per second, it would take you more than 4 trillion years to count this high. So you can see the Earth is very large indeed.