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WD_086/ 2005
(  Satoshi Kinoshita )
| Series: | Works on paper: Drawings | | Medium: | oil pastel on paper | | Size (inches): | 29.6 x 21.8 | | Size (mm): | 760 x 560 | | Catalog #: | WD_086 | | Description: | Signed, date and copyright in pencil on the reverse.
Measure the Earth with Shadows:
More than 2000 years ago, the Greek scientist Eratosthenes first measured the circumference of the Earth with an ingenious technique requiring only sticks, shadows and a little mathematics. This past Spring, over 700 schools from all over North America participated in recreating this momentous experiment in celebration of the World Year of Physics 2005. Thank you to all our participants who made this such a successful project. The Grand Average, calculated from all the submitted answers, appears below.
Eratosthenes and His Experiment:
Contrary, to popular opinion, Columbus was not the first person to proclaim that the Earth is round. The Greeks, among others, had deduced the shape of the Earth more than a thousand years earlier, and the ancient Greek scholar, Eratosthenes, calculated the circumference of the world with surprising accuracy.
Eratosthenes was born in 276 BC in a region of northern Africa that is now part of Libya. He studied in Athens, and was the third head librarian of the great library of Alexandria. In addition to calculating the Earth's circumference, Eratosthenes is remembered for his method of finding prime numbers (the Sieve of Eratosthenes), measuring the distance from the Earth to the Sun and the Moon, and numerous, detailed maps of the world as it was known at the time.
Although Eratosthenes was a brilliant scientist, he lived at a time of many notable Grecian scholars, including his good friend Archimedes, who was one of the greatest mathematicians in history. As a result, Eratosthenes earned the nickname Beta, the second letter in the Greek alphabet, from some of his envious contemporaries who claimed that he was second best among his peers in everything. But history shows that he was a leader in numerous fields including astronomy, geography, literature, poetry, philosophy, and mathematics. Even if he was only second best at so many things, in an era of amazing progress in the sciences and arts, Eratosthenes is clearly among the foremost geniuses of all time.
The World Year of Physics project "Measure the Earth with Shadows," commemorates Eratosthenes' many outstanding accomplishments by giving high school students a chance to duplicate the brilliant scientist's most famous experiment, on the largest scale ever attempted. In 2005, participating students will use shadows to measure the position of the sun at high noon. By comparing their measurements with those of students at other latitudes, they will be able to calculate the size of the Earth, just as Eratosthenes did more than two thousand years ago.
Modern scholars are uncertain of the precise value of the Earth's circumference that Eratosthenes calculated because he recorded his result in units called stadia. We don't know how long Eratosthenes' stadia were, but current estimates suggest that his value of 252,000 stadia is equivalent to a circumference somewhere between 39,690 and 46,620 kilometers. Can 21st century high school students measure the size of our planet any better than a Greek scientist living two millennia ago did? Thanks to the World Year of Physics, we'll find out in 2005.
Are you a high school teacher, or the parent of a high school level, home-schooled child? If so, consider adding the World Year of Physics project "Measure the Earth with Shadows" to your lesson plans next year.
-www.physics2005.org
In this lecture, we shall show how the Greeks made the first real measurements of astronomical distances---the size of the earth and the distance to the moon, both determined quite
accurately, and the distance to the sun, where their best estimate fell short by a factor of two.
How big is the Earth?
The first reasonably good measurement of the earth's size was done by Eratosthenes, a Greek who lived in Alexandria, Egypt, in the third century B.C. He knew that far to the south, in the town of Syene (present-day Aswan, where there is now a huge dam on the Nile) there was a deep well and at midday on June 21, the sunlight reflected off the water far down in this well, something that happened on no other day of the year. The point was that the sun was exactly vertically overhead at that time, and at no other time in the year. Eratosthenes also knew that the sun was never vertically overhead in Alexandria, the closest it got was on June 21, when it was off by an angle he found to be about 7.2 degrees, by measuring the shadow of a vertical stick.
The distance from Alexandria to Syene was measured at 5,000 stades (a stade being 500 feet), almost exactly due south. From this, and the difference in the angle of sunlight at midday on June 21, Eratosthenes was able to figure out how far it would be to go completely around the earth.
-Michael Fowler (UVa Physics Department)/galileoandeinstein.physics.virginia.edu
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