The mathematician and astronomer Eratosthenes is well-known for his technique in finding prime numbers called the “Sieve of Eratosthenes” and he is also known for closely approximating the circumference of the Sun.
Eratosthenes was born in Cyrene, Greece in 276 BC, which is now known Libya in North Africa. He studied in Athens, but then Ptolemy III, the ruler of Cyrene at the time, appointed Eratosthenes head librarian in the Great Library at Alexandria University (now in Egypt). Eratosthenes method of the prime number sieve is used as an important tool in number theory research, and he was the first person to successfully measure the circumference of the Earth quite accurately. When he was about 80 years old, he went blind and because of this blindness he decided to starve himself to death.
Eratosthenes was born in Cyrene, Greece in 276 BC, which is now known Libya in North Africa. He studied in Athens, but then Ptolemy III, the ruler of Cyrene at the time, appointed Eratosthenes head librarian in the Great Library at Alexandria University (now in Egypt). Eratosthenes method of the prime number sieve is used as an important tool in number theory research, and he was the first person to successfully measure the circumference of the Earth quite accurately. When he was about 80 years old, he went blind and because of this blindness he decided to starve himself to death.
While head librarian in the Great Library at Alexandria, Eratosthenes presented a step-by-step procedure for finding prime numbers up to a given limit that he called the Sieve of Eratosthenes. Let us remember that prime numbers are natural numbers that are only divisible by one and itself. To find these so called primes, Eratosthenes propose to write down all known natural numbers starting from the first prime, which is two, and above and then “sieving out” every multiple of that prime number, and then moving on to the next prime, three, and “sieve out” all the multiples of the new prime which in result cancels out the composite numbers and we are left with the primes; this process could continue on forever. The sieve is a great way to find single digit primes, but this process becomes very tedious to find double or triple digit primes. The sieve is still a great ancient form used to find prime numbers.
Another of Eratosthenes great works is his geometrical method for finding the circumference of the Earth. Details of his work were lost in his treatise On the Measurement of the Earth. Authors J J O’Connor and E F Robertson wrote a great article about Eratosthenes of Cyrene; they mention that details of Eratosthenes “calculations appear in works by other authors such as Cleomedes, Theon of Symyrna, and Strabo” (para.12). Anyways on the summer solstice, Eratosthenes noticed that the sunlight reached down to the bottom of a well in Syene, which is near the city of Aswan in Egypt by the Nile. Then, after he calculated the distance between the well in Syene and the library of Alexandria, he measured the angle of a shadow cast in Alexandria which measured seven degrees. And since sunlight rays are parallel lines, Eratosthenes figured that the shadow cast by the building must a transversal line cutting through the center of the Earth.
Using Euclid’s proposition that alternate-interior-angles are equal, Eratosthenes then knew that the Earth’s arc between Syene and Alexandria is seven degrees.Also, he hired some people to measure the distance between the Syene and Alexandria, and the distance they measure about 800 km. Now using ratios and simple geometric calculations, he concluded that the circumference of the Earth was approximately 41, 000 km (about 25,000 miles).
7° = 800 km
360° C (circumference of the Earth)
C = (800 km * 360°) = 41142.8571429 km
7°Modern circumference of the Earth is 24,901 miles. So, Eratosthenes came real close to actual measurements of the circumference of the Earth which is why he is still remembered as a great astronomer as well.
7° = 800 km
360° C (circumference of the Earth)
C = (800 km * 360°) = 41142.8571429 km
7°Modern circumference of the Earth is 24,901 miles. So, Eratosthenes came real close to actual measurements of the circumference of the Earth which is why he is still remembered as a great astronomer as well.
Eratosthenes is revered for his two great contributions in mathematics and astronomy: the Sieve of Eratosthenes and measuring the circumference of the Earth. The sieve is still used in modern number theory research. His scientific calculations for measuring the circumference of the Earth have awarded him with recognition beyond he and his peers could ever dream of. His early studies in Geometry helped him see the connections necessary in order for him to do what many people behind his time have failed to do.
Reference/Sources
O’Coonor, J J and Robertson, E F. “Eratosthenes of Cyrene” School of Mathematics and
Statistics University of St Andrews, Scotland. Jan. 1999. Web. 5 Feb. 2014. http://www-history.mcs.st-andrews.ac.uk/Biographies/Eratosthenes.html
Rosenberg, Matt. “Eratosthenes” About.com. no date. Web. 5 Feb. 2014. <
http://geography.about.com/od/historyofgeography/a/eratosthenes.htm>
http://www.math.wichita.edu/history/men/eratosthenes.html
O’Coonor, J J and Robertson, E F. “Eratosthenes of Cyrene” School of Mathematics and
Statistics University of St Andrews, Scotland. Jan. 1999. Web. 5 Feb. 2014. http://www-history.mcs.st-andrews.ac.uk/Biographies/Eratosthenes.html
Rosenberg, Matt. “Eratosthenes” About.com. no date. Web. 5 Feb. 2014. <
http://geography.about.com/od/historyofgeography/a/eratosthenes.htm>
http://www.math.wichita.edu/history/men/eratosthenes.html