Eratosthenes calculated the circumference of the Earth without leaving Egypt. He knew that at local noon on the summer solstice in Syene (modern Aswan, Egypt), the Sun was directly overhead. He knew this because the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. He measured the Sun’s angle of elevation at noon on the same day in Alexandria. The method of measurement was to make a scale drawing of that triangle which included a right angle between a vertical rod and its shadow. This turned out to be about 7°, or 1/50th of the way around a circle. Taking the Earth as spherical, and knowing both the distance and direction of Syene, he concluded that the Earth’s circumference was fifty times that distance.
His knowledge of the size of Egypt was founded on the work of many generations of surveying trips. Pharaonic bookkeepers gave a distance between Syene and Alexandria of 5,000 stadia (a figure that was checked yearly). Some say that the distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. Carl Sagan says that Eratosthenes paid a man to walk and measure the distance. Some claim Eratosthenes used the Olympic stade of 176.4 m, which would imply a circumference of 44,100 km, an error of 10%, but the 184.8 m Italian stade became (300 years later) the most commonly accepted value for the length of the stade, which implies a circumference of 46,100 km, an error of 15%. It was unlikely, even accounting for his extremely primitive measuring tools, that Eratosthenes could have calculated an accurate measurement for the circumference of the Earth. He made three important assumptions (none of which is perfectly accurate):
- That the distance between Alexandria and Syene was 5000 stadia,
- That the Earth is a perfect sphere.
- That light rays emanating from the Sun are parallel.
Eratosthenes later rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia, likely for reasons of calculation simplicity as the larger number is evenly divisible by 60. In 2012, Anthony Abreu Mora repeated Eratosthenes’ calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference of the Earth.
Seventeen hundred years after Eratosthenes’ death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe, based on a map by Toscanelli, that the Earth’s circumference was one-third smaller. Had Columbus set sail knowing that Eratosthenes’ larger circumference value was more accurate, he would have known that the place that he made landfall was not Asia, but rather the New World.
In 1992 Dr. Lang became the first Westerner ever invited to address the Nippon Origami Association’s annual meeting; he has since been an invited guest at international origami conventions around the world.
- Heat transfer can alter system states;
- Bodies don’t “contain” heat; heat is identified as it comes across system boundaries;
- The amount of heat needed to go from one state to another is path dependent;
- Adiabatic processes are ones in which no heat is transferred.
H = Ht + Hv + Hi (1)
H = overall heat loss
Ht = heat loss due to transmission through walls, windows, doors, floors and more
Hv = heat loss caused by ventilation
Hi = heat loss caused by infiltration