Eratosthenes was a Greek mathematician, geographer, poet and astronomer. He was born in 276 BC in Cyrene, Libya and later studied in Athens under various philosophers. In 245 BC, he became the chief librarian at the Great Library of Alexandria in Egypt. There, he made several contributions such as calculating the circumference of Earth and devising the sieve of Eratosthenes for finding prime numbers. He also created the first map of the world incorporating parallels and meridians. Eratosthenes was considered one of the most learned people of his time with works on many topics from mathematics to chronology.

1. St. Mary High School
FA :-1
Mathematics
Task No.1
Topic:- Biography of Great
Mathematician

2. Eratosthenes
The Great Mathematician

3. Eratosthenes
• Born276 BC
Cyrene
• Died194 BC
Alexandria
• Ethnicity :- Greek
• Occupation:-
• Scholar
• Librarian
• Poet
• Inventor

4. *The son of Aglaos, Eratosthenes was born in
276 BC, in Cyrene. Now part of modern-
day Libya, Cyrene had been founded by the
Greeks centuries earlier, and became the
capital of Pentapolis (North Africa), a country
of five cities: Cyrene, Arsinde, Berenice,
Ptolemias, and Apollonian,
Cyrenaica. Alexander the Great conquered
Cyrene in 332 BC, and following his death in
323 BC its rule was given to one of his
generals, Ptolemy I Soter, the founder of
the Ptolemaic Kingdom
life

5. Continue
*Eratosthenes went to Athens to further his studies. There he was
taught Stoicism by its founder, Zeno of Citium, in philosophical
lectures on living a virtuous life.[9] He then studied
under Ariston of Chios, who led a more cynical school of
philosophy. He also studied under the head of the Platonic
Academy, who was Arcesilaus of Pitane. His interest in Plato led
him to write his very first work at a scholarly level, Platonikos,
inquiring into the mathematical foundation of Plato's
philosophies.[10] Eratosthenes was a man of many perspectives
and investigated the art of poetry under Callimachus.[11] He had
talent as a most imaginative poet.

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*He wrote poems: one in hexameters called Hermes illustrating
the god's life history; and another, in elegiacs, called Erigone,
describing the suicide of the Athenian maiden Erigone
(daughter of Icarius).[12] He wrote Chronographies, a text that
scientifically depicted dates of importance, beginning with
the Trojan War. This work was highly esteemed for its
accuracy: George Syncellus was later able to preserve from
Chronographies a list of 38 kings of the Egyptian Thebes.
Eratosthenes also wrote Olympic Victors, a chronology of the
winners of the Olympic Games. It is not known when he wrote
his works, but they highlighted his abilities.

7. Continue
*These works and his great poetic abilities led the
pharaoh Ptolemy III Euergetes to seek to place him as a
librarian at the Library of Alexandria in the year 245 BC.
Eratosthenes, then thirty years old, accepted Ptolemy's
invitation and travelled to Alexandria, where he lived for
the rest of his life. Within about five years he became
Chief Librarian, a position that the poet Apollonius
Rhodius had previously held. As head of the library
Eratosthenes tutored the children of Ptolemy,
including Ptolemy IV Philopator who became the fourth
Ptolemaic pharaoh.

8. Continue
*Eratosthenes made several important contributions
to mathematics and science, and was a friend
of 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 (modern Aswan, Egypt).

9. Continue
*Eratosthenes believed there was good and bad in
every nation and criticized Aristotle for arguing that
humanity was divided into Greeks and barbarians,
and that the Greeks should keep themselves racially
pure.[14] As he 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 the age of 82 in his
beloved Alexandria.[15]

10. Measurement of the Earth's circumference
*Eratosthenes calculated the circumference of the Earth without
leaving Egypt. He knew that at local noon on the summer
solstice in Syene (modern Aswan, Egypt), the Sun was directly
overhead. 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 measured the Sun's
angle of elevation at noon on the same day in Alexandria. The
method of measurement was to make a scale drawing of that
triangle which included a right angle between a vertical rod
and its shadow. This turned out to be 1/50th 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.

11. Continue

12. Continue
* Some claim Eratosthenes used the Olympic stade of
176.4 m, which would imply a circumference of
44,100 km, an error of 10%,[16] but the 184.8 m Italian
stade became (300 years later) the most commonly
accepted value for the length of the stade,[16] which
implies a circumference of 46,100 km, an error of
15%.[16] 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 for three important
assumptions he made (none of which are perfectly
accurate):[17][16]

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• That Alexandria and Syene lay on the same meridian,
• That the distance between Alexandria and Syene was
5000 stades,
• That the Earth was a perfect sphere.
• 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.[16] Repeating Eratosthenes' calculation
with more accurate data, the result is 40,074 km,
which is 66 km different (0.16 %) from the currently
accepted polar circumference of the Earth.[17]

14. Continue
• Seventeen hundred years after Eratosthenes'
death, while Christopher Columbus studied what
Eratosthenes had written about the size of the
Earth, he chose to believe, based on a map
by Toscanelli, that the Earth's circumference
was one-third smaller. Had Columbus set sail
knowing that Eratosthenes' larger circumference
value was more accurate, he would have known
that the place that he made landfall was not Asia,
but rather a New World.[18]

15. Achievements
• Eusebius of Caesarea in his Preparation 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.

16. Continue
• 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.[23] The actual figure is approximately 109
times.[25]
• 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.[26]

17. Continue
• 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.[27] 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.[28]

18. Prime numbers

19. Continue
• Eratosthenes proposed a simple algorithm for finding prime
numbers. This algorithm is known in mathematics as the Sieve of
Eratosthenes.
• In mathematics, the sieve of Eratosthenes (Greek: κόσκινον
Ἐρατοσθένους), one of a number of prime number sieves, is a
simple, ancient algorithm for finding all prime numbers up to any
given limit. It does so by iteratively marking as composite, i.e., not
prime, the multiples of each prime, starting with the multiples of 2.
The multiples of a given prime are generated starting from that
prime, as a sequence of numbers with the same difference, equal to
that prime, between consecutive numbers. This is the sieve's key
distinction from using trial division to sequentially test each
candidate number for divisibility by each prime.

20. 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.

21. Titles
• Platonikos
• Hermes
• Erigone
• Chronographies
• Olympic Victors
• Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the
Earth)[30] (lost, summarized by Cleomedes)
• Гεωγραϕικά (Geographika)[31] (lost, criticized by Strabo)
• Arsinoe (a memoir of queen Arsinoe; lost; quoted by Athenaeus in
the Deipnosophistae)
• Ariston (concerning Aristo of Chios' addiction to luxury); lost; quoted
by Athenaeus in the Deipnosophistae)[32]
• A fragmentary collection of Hellenistic myths about the constellations,
called Catasterismi (Katasterismoi), was attributed to Eratosthenes,
perhaps to add to its credibility.

22. Modern Implications of Eratosthenes’ Math
• The most actively used discovery of Eratosthenes’ is the leap
day, which adds an extra day onto every fourth year in order
to keep the calendar system accurate.
• We also know the circumference of the earth due to his math
and have been able to calculate how long trips may take
around the world based on his findings.
• Another way we use Eratosthenes’ math is to know how far
away the sun is from Earth. Due to this it is possible to, say,
know how far a planet must be from a star to sustain life, and
other associated equations.
• We also know the tilt of Earth’s axis thanks to Eratosthenes
and thus have been able to figure out how the day and night
cycle works based on his math.

23. Made By
• Preshit . Pegadpalliwar
• Ritik . Atram
• Aniket . Fale
• Sanket . Raut
• Pooja . Jaiswal
• Amisha . Mankar
• Priya . Tapkire
• Shreya .Atram