Eratosthenes

Eratosthenes of Cyrene (c. 276 BCE - c. 194 BCE) was a Greek mathematician and geographer. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today.

He is best known for being the first person to calculate the circumference of the Earth, which he did by comparing altitudes of the mid-day sun at two places a known North-South distance apart. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis, again with remarkable accuracy. Additionally, he may have accurately calculated the Astronomical Unit, or AU, and invented the leap day. He created the first world map, incorporating parallels and meridians based on the available geographic knowledge of his era.

He was a figure of influence in many fields. His devotees nicknamed him Pentathlos after the Olympians who were well-rounded athletes, for he had proven himself to be knowledgeable in every area of learning. Eratosthenes yearned to understand the complexities of the entire world.

Life

Eratosthenes was born in 276 BCE to his father, Aglaos, in the city of Cyrene (modern-day Libya). His name comes from the Greek erato, "loved, beloved," and sthenos, vigor, strength. Cyrene was the capital of Pentapolis, a region of Greek colonies in North Africa. It was a large economic, cultural, and intellectual center. Eratosthenes studied at the local gymnasium, which taught physical skills as well as mathematics, linguistics, and music.

Eratosthenes went to Athens to further his studies. He studied under various academics, including Zeno of Citium, the founder of the philosophy of Stoicism; the philosopher Aristo of Chios; the head of the Platonic Academy, Arcesilaus of Pitane; the poet, Callimachus, among others. In this early period, he wrote his first works, including Platonikos, a mathematical examination of Plato's early works; Hermes and Erigone, poems of Greek mythology; Chronographies, an accurate chronology from the time of the Trojan War; and Olympic Victors, a chronology of victors in the Olympic Games.

These early works and his poetic abilities led the pharaoh Ptolemy III Euergetes to place him as a librarian at the Library of Alexandria in the year 245 BC. Eratosthenes was thirty years old at the time. He traveled to Alexandria and lived there for the rest of his life. Within about five years he became Chief Librarian, and tutored the children of Ptolemy, including Ptolemy IV Philopator who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication. It was said that these were copied so accurately that it was impossible to tell if the library had returned the original or the copy. Eratosthenes created a whole section devoted to the examination of Homer, and acquired original works of great tragic dramas of Aeschylus, Sophocles and Euripides.

Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes, the great mathematician. Around 255 BCE, he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, the later astronomer Cleomedes credited him with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the Sun at noon on the summer solstice in Alexandria and on Elephantine Island near modern Aswan, Egypt.

As Eratosthenes aged he contracted ophthalmia, becoming blind around 195 BC. Losing the ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194 BC at 82 in Alexandria.

Measurement of the Earth's circumference

File:Eratosthenes measure of Earth circumference.svg

Illustration showing a portion of the globe showing a part of the African continent. The sunbeams shown as two rays hitting the ground at Syene and Alexandria. Angle of sunbeam and the gnomons (vertical pole) is shown at Alexandria, which allowed Eratosthenes' estimates of radius and circumference of Earth.

Eratosthenes calculated the Earth's circumference without leaving Egypt. He knew that at local solar noon on the summer solstice in Syene (today Aswan) Egypt, the Sun was directly overhead. (Syene is at latitude 24°05′ North, near to the Tropic of Cancer, which was 23°42′ North in 100 BC) 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 then measured the Sun's angle of elevation at noon in Alexandria by using a vertical rod, known as a gnomon, and measuring the length of its shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This turned out to be about 7°, or 1/50th the circumference of 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 historians say that the distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. 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 five important assumptions (none of which is perfectly accurate):

1. That the distance between Alexandria and Syene was 5000 stadia,
2. That Alexandria is due north of Syene
3. That Syene is on the Tropic of Cancer
4. That the Earth is a perfect sphere.
5. 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's 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.

"Father of geography"

19th-century reconstruction of Eratosthenes' map of the (for the Greeks) known world, c. 194 BC

Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of information and representations of the world that needed to be pieced together in some organized format. In his three-volume work Geography, he described and mapped his entire known world, even dividing the Earth into five climate zones: two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics. He had invented geography. He created terminology that is still used today. He placed grids of overlapping lines over the surface of the Earth. He used parallels and meridians to link together every place in the world. It was now possible to estimate one's distance from remote locations with this network over the surface of the Earth. In the Geography the names of over 400 cities and their locations were shown: this had never been achieved before. Unfortunately, his Geography has been lost to history, but fragments of the work can be pieced together from other great historians like Pliny the Elder, Polybius, Strabo, and Marcianus.

• The first book was something of an introduction and gave a review of his predecessors, recognizing their contributions that he compiled in the library. In this book Eratosthenes denounced Homer as not providing any insight into what he now described as geography. His disapproval of Homer's topography angered many who believed the world depicted in the Odyssey to be legitimate. He also commented on the ideas of the nature and origin of the Earth: he had thought of Earth as an immovable globe; while on its surface was a place that was changing. He had hypothesized that at one time the Mediterranean was a vast lake that covered the countries that surrounded it; and had only become connected to the ocean to the west when a passage had opened up sometime in its history.
• In the second book is his discovery about the circumference of the Earth. This is where, according to Pliny, "The world was grasped." Eratosthenes described his famous story of the well in Syene, described above. This book would now be considered a text on mathematical geography.
• His third book of the Geography contained political geography. He cited countries and used parallel lines to divide the map into sections, to give accurate descriptions of the realms. This was a breakthrough, and can be considered the beginning of geography.

Achievements

Eratosthenes was described by the Suda Lexicon as a Πένταθλος (Pentathlos), meaning "athlete of five(sports)", or can be translated as "All-Rounder", for he was skilled in a variety of things: He was a true polymath. He was nicknamed Beta because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians.

• Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the Sun to be "σταδίων μυριάδας τετρακοσίας καὶ ὀκτωκισμυρίας" (literally "of stadia myriads 400 and 80,000") and the distance to the Moon to be 780,000 stadia. The expression for the distance to the Sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974–1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad. With a stade of 185 m, 804,000,000 stadia is 149,000,000 km, approximately the distance from the Earth to the Sun.
• Eratosthenes also calculated the Sun's diameter. According to Macrobious, Eratosthenes made the diameter of the Sun to be about 27 times that of the Earth. The actual figure is approximately 109 times.
• During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.
• He was also very proud of his solution for Doubling the Cube. His motivation was that he wanted to produce catapults. Eratosthenes constructed a mechanical line drawing device to calculate the cube, called the mesolabio. He dedicated his solution to King Ptolemy, presenting a model in bronze with it a letter and an epigram. Archimedes was Eratosthenes' friend and he, too, worked on the war instrument with mathematics. Archimedes dedicated his book The Method to Eratosthenes, knowing his love for learning and mathematics.

Works

Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at the Library. He wrote on many topics — geography, mathematics, philosophy, chronology, literary criticism, grammar, poetry, and even old comedies. Unfortunately, there are only fragments left of his works after the Destruction of the Library of Alexandria.

Titles

• Platonikos
• Hermes
• Erigone
• Chronographies
• Olympic Victors
• Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth) (lost, summarized by Cleomedes)
• Гεωγραϕικά (Geographika) (lost, criticized by Strabo)
• Arsinoe (a memoir of queen Arsinoe III of Egypt; lost; quoted by Athenaeus in the Deipnosophistae)
• Ariston (concerning Aristo of Chios's addiction to luxury); lost; quoted by Athenaeus in the Deipnosophistae)
• A fragmentary collection of Hellenistic myths about the constellations, called Catasterismi (Katasterismoi), was attributed to Eratosthenes, perhaps to add to its credibility.

See also

Eponyms

• Eratosthenes crater on the Moon
• Eratosthenian period in the lunar geologic timescale
• Eratosthenes Seamount in the eastern Mediterranean Sea

Further reading

• Aujac, G. (2001). Eratosthène de Cyrène, le pionnier de la géographie. Paris: Édition du CTHS. 224p.
• Bulmer-Thomas, Ivor (1939–1940). Selections Illustlating the History of Greek Mathematics. Cambridge, Massachusetts: Harvard University Press. 
• Diller, A (1934). "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". Klio 27 (3): 258–269. 
• Dorofeeva, A. V. (1988). "Eratosthenes (ca. 276–194 B.C.)" (in Russian). Mat. V Shkole (4): i. 
• Dutka, J. (1993). "Eratosthenes' measurement of the Earth reconsidered". Arch. Hist. Exact Sci. 46 (1): 55–66. doi:10.1007/BF00387726. 
• El'natanov, B. A. (1983). "A brief outline of the history of the development of the sieve of Eratosthenes" (in Russian). Istor.-Mat. Issled. 27: 238–259. 
• Fischer, I (1975). "Another look at Eratosthenes' and Posidonius' determinations of the Earth's circumference". Quarterly Journal of the Royal Astronomical Society 16: 152–167. Bibcode: 1975QJRAS..16..152F. http://articles.adsabs.harvard.edu//full/1975QJRAS..16..152F/0000152.000.html. 
• Fowler, D. H.; Rawlins, Dennis (1983). "Eratosthenes' ratio for the obliquity of the ecliptic". Isis 74 (274): 556–562. doi:10.1086/353361. 
• Fraser, P. M. (1970). "Eratosthenes of Cyrene". Proceedings of the British Academy 56: 175–207. 
• Fraser, P. M. (1972). Ptolemaic Alexandria. Oxford: Clarendon Press. 
• Fuentes González, P. P., "Ératosthène de Cyrène", in R. Goulet (ed.), Dictionnaire des Philosophes Antiques, vol. III, Paris, Centre National de la Recherche Scientifique, 2000, pp. 188–236.
• Geus K. (2002). Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftgeschichte. München: Verlag C.H. Beck. (Münchener Beiträge zur Papyrusforschung und antiken Rechtsgeschichte. Bd. 92) X, 412 S.
• Goldstein, B. R. (1984). "Eratosthenes on the "measurement" of the Earth". Historia Math. 11 (4): 411–416. doi:10.1016/0315-0860(84)90025-9. 
• Gulbekian, E. (1987). "The origin and value of the stadion unit used by Eratosthenes in the third century B.C". Archive for History of Exact Sciences 37 (4): 359–363. doi:10.1007/BF00417008. 
• Honigmann, E. (1929). Die sieben Klimata und die πολεις επισημοι. Eine Untersuchung zur Geschichte der Geographie und Astrologie in Altertum und Mittelalter. Heidelberg: Carl Winter's Universitätsbuchhandlung. 247 S.
• Knaack, G. (1907). "Eratosthenes". Pauly–Wissowa VI: 358–388. 
• Manna, F. (1986). "The Pentathlos of ancient science, Eratosthenes, first and only one of the "primes"" (in Italian). Atti Accad. Pontaniana (N.S.) 35: 37–44. 
• Muwaf, A.; Philippou, A. N. (1981). "An Arabic version of Eratosthenes writing on mean proportionals". J. Hist. Arabic Sci. 5 (1–2): 147–174. 
• Nicastro, Nicholas (2008). Circumference: Eratosthenes and the ancient quest to measure the globe. New York: St. Martin's Press. ISBN 0-312-37247-7. 
• Template:MacTutor Biography
• Marcotte, D. (1998). "La climatologie d'Ératosthène à Poséidonios: genèse d'une science humaine". G. Argoud, J.Y. Guillaumin (eds.). Sciences exactes et sciences appliquées à Alexandrie (IIIe siècle av J.C. – Ier ap J.C.). Saint Etienne: Publications de l'Université de Saint Etienne: 263–277.
• McPhail, Cameron (2011). Reconstructing Eratosthenes' Map of the World: a Study in Source Analysis. A Thesis Submitted for the Degree of Master of Arts at the University of Otago. Dunedin, New Zealand.
• Pfeiffer, Rudolf (1968). History of Classical Scholarship From the Beginnings to the End of the Hellenistic Age. Oxford: Clarendon Press. 
• Rawlins, D. (1982). "Eratosthenes' geodesy unraveled : was there a high-accuracy Hellenistic astronomy". Isis 73 (2): 259–265. doi:10.1086/352973. 
• Rawlins, D. (1982). "The Eratosthenes – Strabo Nile map. Is it the earliest surviving instance of spherical cartography? Did it supply the 5000 stades arc for Eratosthenes' experiment?". Arch. Hist. Exact Sci. 26 (3): 211–219. 
• Rawlins, D. (2008). "Eratosthenes's large Earth and tiny universe" (PDF). DIO 14: 3–12. Bibcode: 2008DIO....14....3R. http://www.dioi.org/vols/we0.pdf. 
• Roller, Duane W. (2010). Eratosthenes' Geography: Fragments collected and translated, with commentary and additional material. Princeton: Princeton University Press. ISBN 978-0-691-14267-8. https://books.google.com/books?id=8peKyWK_SWsC. 
• Shcheglov, D.A. (2004/2006). "Ptolemy's System of Seven Climata and Eratosthenes' Geography". Geographia Antiqua 13: 21–37.
• Shcheglov, D.A. (2006). "Eratosthenes' Parallel of Rhodes and the History of the System of Climata". Klio 88 (2): 351–359. doi:10.1524/klio.2006.88.2.351. https://www.academia.edu/191065/Eratosthenes_Parallel_of_Rhodes_and_the_History_of_the_System_of_Climata. 
• Strabo (1917). The Geography of Strabo. Horace Leonard Jones, trans. New York: Putnam. 
• Taisbak, C. M. (1984). "Eleven eighty-thirds. Ptolemy's reference to Eratosthenes in Almagest I.12". Centaurus 27 (2): 165–167. doi:10.1111/j.1600-0498.1984.tb00766.x. Bibcode: 1984Cent...27..165T. 
• Thalamas, A. (1921). La géographe d'Ératosthène. Versailles.
• Wolfer, E. P. (1954). Eratosthenes von Kyrene als Mathematiker und Philosoph. Groningen-Djakarta.