1. Erastosthenes: Measuring the Size of the Earth Scott Morrison 8.282J / 12.402J 5 Feb 2009

2. Erastosthenes of Cyrene (275 - 194 B.C.) Chief librarian of Alexandria from 240 B.C. until his death His goal: to “reform the map of the world” in a systematic way Most famous for giving a good estimate for the Earth's size

3. Erastosthenes of Cyrene (275 - 194 B.C.) The world as described by Herodotus, ca. 450 B.C.

4. Erastosthenes of Cyrene (275 - 194 B.C.) Erastosthenes' improvements to the world map, 194 B.C.

5. Erastosthenes of Cyrene (275 - 194 B.C.) The Greeks had known several earth models by 500 B.C.  Homer: disk-shaped earth, heavenly dome  Pythagoras: ball-shaped earth, celestial sphere Again, our observations of the stars make it evident, not only that the earth is circular, but that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward”  Aristotle, “On the Heavens”, Book II, Chapter 14

6. Erastosthenes of Cyrene (275 - 194 B.C.) Obvious question: how big? Observations:  At Syene, no shadows  At Alexandria, 1/50 of circle  Distance is 5000 stades Assumptions:  Earth is a perfect sphere  Sun's rays parallel  Syene is due south of Alex. 250,000 stades = 39,700 to 45,000 km Actual: 40,075 km

7. Erastosthenes of Cyrene (275 - 194 B.C.) How good are these measurements?  Syene is actually 30' north of Tropic or Cancer  Actual angle between cities is 7' less than stated  True distance is 5,300 stades by road—4,530 stades directly Assumptions?  Oblate spheroid: error is 1 part in 300  Rays are parallel to 1 part in 100,000  2° longitude between the two—so effective distance is 5% less Whichever definition of a stade you use, error is about 10%.

8. Erastosthenes of Cyrene (275 - 194 B.C.) An amusing story about Columbus and his trip to Japan America:  Marinus of Tyre (ca. 70 - 130 A.D.) got a circumference 20% smaller. He wrote that the “terrestrial landmass” (i.e. Eurasia) subtended five-eighths of Earth, leaving only 135° of ocean.  Al-Farghani: 1 degree = Arabic miles (1830 m). Columbus used Italian miles (1238 m) instead.  Result: he thought the distance to the Orient was 3,700 km, not 19,600 km.