Eratosthenes
Encyclopedia
Eratosthenes of Cyrene
was a Greek mathematician
, poet
, athlete, geographer
, astronomer
, and music theorist.
He was the first person to use the word "geography" and invented the discipline of geography as we understand it. He invented a system of latitude
and longitude
.
He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun
and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy
.
According to an entry in the Suda
(a 10th century reference), his contemporaries nicknamed him beta, from the second letter of the Greek alphabet, because he supposedly proved himself to be the second best in the world in almost every field.
Eratosthenes was born in Cyrene (in modern-day Libya
). He was the third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient world, and died in the capital of Ptolemaic Egypt
.
Eratosthenes studied in Alexandria, and claimed to have also studied for some years in Athens
. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library
, succeeding the second librarian, Apollonius of Rhodes
, in that post. He made several important contributions to mathematics
and science
, and was a good friend to Archimedes
. Around 255 BC he invented the armillary sphere
.
In On the Circular Motions of the Celestial Bodies, 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 Syene (now Aswan
, Egypt).
Eratosthenes criticized Aristotle
for arguing that humanity was divided into Greeks and barbarian
s, and that the Greeks should keep themselves racially pure, believing there was good and bad in every nation. By 195 BC, Eratosthenes became blind
. He died in 194 BC at the age of 82.
of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice
at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer
, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc
distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5000 stadia
(about 500 geographical miles or 800 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.
Although Eratosthenes' method was well founded, the accuracy of his calculation was limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. Given the margin of error for each of these aspects of his calculation, the accuracy of Eratosthenes' size of the Earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth's size was accepted for hundreds of years afterwards. His method was used by Posidonius
about 150 years later.
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 "" (literally "of stadia myriad
s 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 stadium of 185 meters, 804,000,000 stadia is 149,000,000 kilometers, the modern distance.
for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes
.
Cyrene, Libya
Cyrene was an ancient Greek colony and then a Roman city in present-day Shahhat, Libya, the oldest and most important of the five Greek cities in the region. It gave eastern Libya the classical name Cyrenaica that it has retained to modern times.Cyrene lies in a lush valley in the Jebel Akhdar...
was a Greek mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, poet
Poet
A poet is a person who writes poetry. A poet's work can be literal, meaning that his work is derived from a specific event, or metaphorical, meaning that his work can take on many meanings and forms. Poets have existed since antiquity, in nearly all languages, and have produced works that vary...
, athlete, geographer
Geographer
A geographer is a scholar whose area of study is geography, the study of Earth's natural environment and human society.Although geographers are historically known as people who make maps, map making is actually the field of study of cartography, a subset of geography...
, astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
, and music theorist.
He was the first person to use the word "geography" and invented the discipline of geography as we understand it. He invented a system of latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
.
He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy
Troy
Troy was a city, both factual and legendary, located in northwest Anatolia in what is now Turkey, southeast of the Dardanelles and beside Mount Ida...
.
According to an entry in the Suda
Suda
The Suda or Souda is a massive 10th century Byzantine encyclopedia of the ancient Mediterranean world, formerly attributed to an author called Suidas. It is an encyclopedic lexicon, written in Greek, with 30,000 entries, many drawing from ancient sources that have since been lost, and often...
(a 10th century reference), his contemporaries nicknamed him beta, from the second letter of the Greek alphabet, because he supposedly proved himself to be the second best in the world in almost every field.
Life
Libya
Libya is an African country in the Maghreb region of North Africa bordered by the Mediterranean Sea to the north, Egypt to the east, Sudan to the southeast, Chad and Niger to the south, and Algeria and Tunisia to the west....
). He was the third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient world, and died in the capital of Ptolemaic Egypt
Ptolemaic Egypt
Ptolemaic Egypt began when Ptolemy I Soter invaded Egypt and declared himself Pharaoh of Egypt in 305 BC and ended with the death of queen Cleopatra VII of Egypt and the Roman conquest in 30 BC. The Ptolemaic Kingdom was a powerful Hellenistic state, extending from southern Syria in the east, to...
.
Eratosthenes studied in Alexandria, and claimed to have also studied for some years in Athens
Athens
Athens , is the capital and largest city of Greece. Athens dominates the Attica region and is one of the world's oldest cities, as its recorded history spans around 3,400 years. Classical Athens was a powerful city-state...
. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library
Library of Alexandria
The Royal Library of Alexandria, or Ancient Library of Alexandria, in Alexandria, Egypt, was the largest and most significant great library of the ancient world. It flourished under the patronage of the Ptolemaic dynasty and functioned as a major center of scholarship from its construction in the...
, succeeding the second librarian, Apollonius of Rhodes
Apollonius of Rhodes
Apollonius Rhodius, also known as Apollonius of Rhodes , early 3rd century BCE – after 246 BCE, was a poet, and a librarian at the Library of Alexandria...
, in that post. He made several important contributions to mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, and was a good friend to Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
. Around 255 BC he invented the armillary sphere
Armillary sphere
An armillary sphere is a model of objects in the sky , consisting of a spherical framework of rings, centred on Earth, that represent lines of celestial longitude and latitude and other astronomically important features such as the ecliptic...
.
In On the Circular Motions of the Celestial Bodies, Cleomedes
Cleomedes
Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.-Placing his work chronologically:...
credited him with having calculated the Earth's circumference
Circumference
The circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....
around 240 BC, using knowledge of the angle of elevation
Solar elevation angle
The solar elevation angle is the elevation angle of the sun. That is, the angle between the directionof the geometric center of the sun's apparent disk and the horizon...
of the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
at noon on the summer solstice in Alexandria and on Elephantine
Elephantine
Elephantine is an island in the River Nile, located just downstream of the First Cataract at the southern border of Ancient Egypt. This region is referred to as Upper Egypt because the land is higher than that near the Mediterranean coast. The island may have received its name because it was a...
Island near Syene (now Aswan
Aswan
Aswan , formerly spelled Assuan, is a city in the south of Egypt, the capital of the Aswan Governorate.It stands on the east bank of the Nile at the first cataract and is a busy market and tourist centre...
, Egypt).
Eratosthenes criticized Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
for arguing that humanity was divided into Greeks and barbarian
Barbarian
Barbarian and savage are terms used to refer to a person who is perceived to be uncivilized. The word is often used either in a general reference to a member of a nation or ethnos, typically a tribal society as seen by an urban civilization either viewed as inferior, or admired as a noble savage...
s, and that the Greeks should keep themselves racially pure, believing there was good and bad in every nation. By 195 BC, Eratosthenes became blind
Blindness
Blindness is the condition of lacking visual perception due to physiological or neurological factors.Various scales have been developed to describe the extent of vision loss and define blindness...
. He died in 194 BC at the age of 82.
Eratosthenes' measurement of the Earth's circumference
Eratosthenes calculated the circumferenceCircumference
The circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....
of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice
Summer solstice
The summer solstice occurs exactly when the axial tilt of a planet's semi-axis in a given hemisphere is most inclined towards the star that it orbits. Earth's maximum axial tilt to our star, the Sun, during a solstice is 23° 26'. Though the summer solstice is an instant in time, the term is also...
at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer
Tropic of Cancer
The Tropic of Cancer, also referred to as the Northern tropic, is the circle of latitude on the Earth that marks the most northerly position at which the Sun may appear directly overhead at its zenith...
, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5000 stadia
Stadion (unit of length)
The stadion, Latinized as stadium and anglicized as stade, is an ancient Greek unit of length. According to Herodotus, one stade is equal to 600 feet. However, there were several different lengths of “feet”, depending on the country of origin....
(about 500 geographical miles or 800 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m, which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.
Although Eratosthenes' method was well founded, the accuracy of his calculation was limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the Earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable, especially for travel along the non-linear Nile which was traveled primarily by boat. Given the margin of error for each of these aspects of his calculation, the accuracy of Eratosthenes' size of the Earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the Earth's size was accepted for hundreds of years afterwards. His method was used by Posidonius
Posidonius
Posidonius "of Apameia" or "of Rhodes" , was a Greek Stoic philosopher, politician, astronomer, geographer, historian and teacher native to Apamea, Syria. He was acclaimed as the greatest polymath of his age...
about 150 years later.
Other astronomical distances
Eusebius of CaesareaEusebius of Caesarea
Eusebius of Caesarea also called Eusebius Pamphili, was a Roman historian, exegete and Christian polemicist. He became the Bishop of Caesarea in Palestine about the year 314. Together with Pamphilus, he was a scholar of the Biblical canon...
in his Preparatio Evangelica
Preparation for the Gospel
Εὑαγγελικὴ Προπαρασκευή , commonly known by its Latin title Praeparatio evangelica, was a work of Christian apologetics written by Eusebius in the early part of the fourth century AD...
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 "" (literally "of stadia myriad
Myriad
Myriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...
s 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 stadium of 185 meters, 804,000,000 stadia is 149,000,000 kilometers, the modern distance.
Prime numbers
Eratosthenes also proposed a simple algorithmAlgorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes
Sieve of Eratosthenes
In mathematics, the sieve of Eratosthenes , one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to a specified integer....
.
Works
- Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth) (lost, summarized by CleomedesCleomedesCleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies.-Placing his work chronologically:...
) - Geographica (lost, criticized by StraboStraboStrabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...
) - Arsinoe (a memoir of queen ArsinoeArsinoe III of EgyptArsinoe III was Queen of Egypt . She was a daughter of Ptolemy III and Berenice II.Between late October and early November 220 BC she was married to her brother, Ptolemy IV. She took active part in the government of the country, at least in the measure that it was tolerated by the all-powerful...
; lost; quoted by AthenaeusAthenaeusAthenaeus , of Naucratis in Egypt, Greek rhetorician and grammarian, flourished about the end of the 2nd and beginning of the 3rd century AD...
in the DeipnosophistaeDeipnosophistaeThe Deipnosophistae may be translated as The Banquet of the Learned or Philosophers at Dinner or The Gastronomers...
) - A fragmentary collection of Hellenistic myths about the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
s, called CatasterismiCatasterismiCatasterismi is an Alexandrian prose retelling of the mythic origins of stars and constellations, as they were interpreted in Hellenistic culture...
(Katasterismoi), was attributed to Eratosthenes, perhaps to add to its credibility.
Named after Eratosthenes
- Eratosthenes (crater)Eratosthenes (crater)Eratosthenes is a relatively deep lunar impact crater that lies on the boundary between the Mare Imbrium and Sinus Aestuum mare regions. It forms the western terminus of the Montes Apenninus mountain range. The crater has a well-defined circular rim, terraced inner wall, central mountain peaks, an...
on the moonMoonThe Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more... - EratosthenianEratosthenianThe Eratosthenian period in the lunar geologic timescale runs from 3,200 million years ago to 1,100 million years ago. It is named after the crater Eratosthenes, whose formation marks the beginning of this period. The formation of the crater Copernicus marks its end, and the beginning of the...
period in the lunar geologic timescaleLunar geologic timescaleThe lunar geological timescale divides the history of Earth's Moon into five generally recognized periods: the Copernican, Eratosthenian, Imbrian , Nectarian, and Pre-Nectarian... - Eratosthenes SeamountEratosthenes SeamountThe Eratosthenes Seamount is a seamount in the Eastern Mediterranean about 100 km south of western Cyprus. It is a large, submerged massif, about 120 km long and 80 km wide. Its peak lies at the depth of 690 m and it rises 2000 m above the surrounding seafloor, which is located at...
in the eastern Mediterranean Sea
External links
- Bernhardy, Gottfried: "Eratosthenica" Berlin 1822 Reprinted Osnabruck 1968 (German text)
- Bernhardy, Gottfried: Eratosthenica Berlin, 1822 (PDF) (Latin/Greek)
- Eratosthenes' sieve in Javascript
- Eratosthenes' sieve as a simple algorithm
- About Eratosthenes' methods, including a Java applet
- How to measure the earth with Eratosthenes' method
- How the Greeks estimated the distances to the moon and sun
- Eratosthenes on PBS.org
- Measuring the earth with Eratosthenes' method
- List of ancient Greek mathematecians and contemporaries of Eratosthenes
- New Advent Encyclopedia article on the Library of Alexandria
- Eratosthenes' sieve explored and visualised in Flash
- Eratosthenes' sieve in classic BASIC all-web based interactive programming environment
- Following in the footsteps of Eratosthenes : project :fr:La main à la pâte.