Eratosthenes’s Inventions, Early Life, Education and History

Eratosthenes was a Greek mathematician, astronomer, geographer, and poet who lived in the 3rd century BC. He is best known for his inventions such as the sieve of Eratosthenes, the armillary sphere, and the chronograph. He is also known for his discoveries such as the measurement of the Earth’s circumference, the calculation of the tilt of the Earth’s axis, and the identification of the prime meridian.

Early Life and Education

Eratosthenes was born in 276 BC in Cyrene, a Greek colony in present-day Libya. He was the son of Aglaos, a wealthy landowner, and a woman whose name is unknown. He had a brother named Ariston. He showed an early interest in learning and was educated by various tutors and teachers in Cyrene.

Eratosthenes moved to Athens when he was about 20 years old, where he studied at the Academy, the famous school founded by Plato. He learned philosophy, mathematics, astronomy, and poetry from various scholars such as Lysanias, Ariston of Chios, Arcesilaus, and Callimachus. He also became friends with some of the most prominent figures of his time, such as Zeno of Citium, the founder of Stoicism, and Ptolemy II Philadelphus, the king of Egypt.

Inventions and Discoveries

Eratosthenes was a prolific inventor and discoverer who made significant contributions to various fields of knowledge. Some of his inventions and discoveries are:

• The sieve of Eratosthenes: This is a simple algorithm that can find all the prime numbers up to a given limit. The algorithm works by marking off the multiples of each prime number starting from 2, leaving only the prime numbers unmarked. Eratosthenes invented this algorithm in his book ‘On Arithmetic’, which is now lost.
• The armillary sphere: This is a device that can model the celestial sphere and show the positions and motions of the stars and planets. The device consists of a set of rings that represent the equator, the ecliptic, the meridian, and other circles on the sky. Eratosthenes invented this device in his book ‘On the Constellations’, which is also lost.
• The chronograph: This is a device that can measure time intervals and record events. The device consists of a water clock that has a rotating drum with pegs that trigger levers that mark a wax tablet. Eratosthenes invented this device in his book ‘On Inventions’, which is also lost.
• The measurement of the Earth’s circumference: This is one of Eratosthenes’s most famous achievements. He measured the Earth’s circumference by using two observations: first, he knew that on the summer solstice, the sun was directly overhead at Syene (now Aswan) in Egypt; second, he measured the angle of the sun’s shadow at Alexandria in Egypt on the same day. He then used geometry to calculate that the angle was about 7.2 degrees, which corresponds to 1/50th of a circle. He then multiplied this fraction by an estimate of the distance between Syene and Alexandria (about 5000 stadia or 800 km), and obtained an estimate of the Earth’s circumference as 250000 stadia or 40000 km. This estimate was remarkably close to the actual value of about 40075 km.
• The calculation of the tilt of the Earth’s axis: This is another remarkable achievement of Eratosthenes. He calculated the tilt of the Earth’s axis by using two observations: first, he knew that the sun was directly overhead at Syene on the summer solstice; second, he measured the length of the longest day at Alexandria on the same day. He then used trigonometry to calculate that the tilt of the Earth’s axis was about 23.8 degrees, which is very close to the actual value of about 23.4 degrees.
• The identification of the prime meridian: This is another important contribution of Eratosthenes to geography. He identified the prime meridian, which is the line of longitude that passes through Greenwich, England, and defines zero degrees longitude. He chose this line because it passed through Alexandria, Rhodes, and Carthage, which were some of the most important cities of his time. He also divided the Earth into five climatic zones: the torrid zone, the two temperate zones, and the two frigid zones.

Philosophy and Writings

Eratosthenes was also a philosopher and a writer who wrote several books and poems on various topics. Some of his works are:

• ‘Platonicus’: This is a philosophical dialogue that discusses the nature and origin of the Platonic ideas. Eratosthenes defended the Platonic view that the ideas are eternal and independent of the sensible world, against the criticisms of Aristotle and others.
• ‘Hermes’: This is a poem that describes the mythical journey of Hermes, the messenger of the gods, from Olympus to Egypt. Eratosthenes used this poem to convey his knowledge of astronomy, geography, and history.
• ‘Chronicles’: This is a historical work that traces the history of the world from the creation to his own time. Eratosthenes used various sources and methods to synchronize the events and dates of different cultures and regions. He also introduced a new system of dating based on the Olympiads, which are four-year periods starting from 776 BC.

History and Legacy

Eratosthenes lived a long and productive life, working at various institutions such as the Academy, the Library of Alexandria, and the court of Ptolemy III. He died in 194 BC in Alexandria, Egypt, at the age of 82. He was honored by various titles and epithets, such as Beta (the second letter of the Greek alphabet), Pentathlos (the winner of five contests), and Philologos (the lover of learning).

Eratosthenes is widely regarded as one of the greatest and most versatile scholars of all time. He is credited with founding or advancing various disciplines such as geography, chronology, mathematics, astronomy, and literature. His works have inspired and influenced many scholars, scientists, and writers, such as Strabo, Ptolemy, Archimedes, Plutarch, Copernicus, Newton, and Carl Sagan.