Greek Mathematics
Mikaela and Akila
The History of Math
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Mathematics began in the 6th century BC
Pythagoras coined the term mathematics, which came
from the word mathema which means "subject of
instruction"
Greeks: refined the methods and expanded the subject
matter. Chinese: created the place value system. India:
Hindu-Arabic numeral system and the rules for the use
of its operations
From ancient times to the Middle Ages, bursts of
mathematical creativity and stagnation
Since the Renaissance, new mathematical
developments, interacting with new scientific
discoveries, were made at an increasing pace that
The Theorem of Thales
• An angle inscribed in a semicircle is a right
angle
• OA=OB=OC, so triangles OBA and OBC
are isosceles.
• A+(A+B)+B=180
2A+2B=180
2(A+B)=180
(A+B)=90
The Pythagoreans
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Group led by Pythagoras
Credited with discovery of irrational
numbers
Not many people are sure of who found each
discovery-- all credit goes to the leader
The Discovery of Musical
Law
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Pythagoras was looking to determine interval ratios in
music
Using lyre and monochord, he stopped the string exactly
in the middle and produced an octave ratio of 1:2
The universe is a vast lyre
Speed of vibration and size of the
sound producing body
Sound is produced by a vibration in
the air
Vibrational frequency of string is
inversely proportional to length
Eratosthenes
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(276-194 BC)
Greek mathematician, geographer, and
astronomer
Noted for devising a map system based on
latitude and longitude lines and computing
the size of the Earth.
200 BC- thought to have coined or to have
adopted the word geography.
Eratosthenes Experiment
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240 BC
Used trig and knowledge of the angle of
elevation of the sun at noon in Alexandria
and Syene to calculate the Earth's
circumference
Assumed that the Earth is spherical and that
the sun is so far away that its rays can be
taken as parallel.
Some Definitions
Tropic of Cancer: one of the five major circles of latitude
that marks maps of the Earth. The current latitude is 23°
26′ 22″ north of the Equator.
Local noon: when the sun is the highest in the sky; not
necessarily 12 pm on the clock.
Solstice: an astronomical event that happens twice a year
when the tilt of the Earth's axis is most inclined toward
or away from the sun.
In the northern hemisphere, summer solstice: around
June 21 and winter solstice: around December 21.
Just know...
What matters for the experiment is the fact that
on the summer solstice, local noon, the sun
rays are just overhead (at a right angle to the
ground) on the Tropic of Cancer.
Experiment
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He used a vertical stick and
measuring the shadow to find that in
his hometown of Alexandria, the
angle for elevation of the sun would
be 83 degrees.
He then assumed that Alexandria
was due north of Syene, and he used
geometry of parallel lines to find that
the distance from Alexandria to
Syene must be 7/360 of the total
circumference of the Earth.
The distance between the cities was
known from caravan travellings to
be about 5,000 stadia.
His value for the circumference
corresponds to between 39,690 km
and 46,620 km.
Euclid of Alexandria
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Greek mathematician
300 BC
Father of Geometry
His 13 volume Elements was used as a textbook in
almost unchanged form for more than 2000 years, and
is still a basic source.
o It deals with plane and solid geometry, proportion, and properties of
numbers.
He is known to have conducted a school of mathematics
in Alexandria during the reign of Ptolemy I.
The first printed edition of the Elements (1482) was in
Latin, translated from Arabic.
o Sir Henry Billingsley's translation (1570) was the
Euclid's Algorithm
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A way to find the greatest common divisor of two
positive integers.
Example: a=210;b=45
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Divide 210 by 45, and get the result 4 with remainder 30, so 210=4·45+30.
Divide 45 by 30, and get the result 1 with remainder 15, so 45=1·30+15.
Divide 30 by 15, and get the result 2 with remainder 0, so 30=2·15+0.
The greatest common divisor of 210 and 45 is 15.
a=qb+r
Heron
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Greek mathematician, scientist, and inventor
Renowned for his works in mechanics, mathematics,
and physics.
Born in Egypt in the year 20
Died in the year 62
Most of his works accomplished in Alexandria, Egypt.
Well known for his studies in geometry and geodesy (a
branch of math that searches to determine the size and
shape of earth, and the location of objects or areas on
the earth)
Books: Metrica, Automatopoietica, Pneumatica,
Belopoeica, and Cheirobalistra.
Inventions
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He created a water organ, fire engine, coin
operated device, and the aeolipile.
Aeolipile: rotary steam engine that consisted
of a sphere mounted on a boiler and having
two nozzles to produce a rotary motion from
the escaping steam.
The siphon, known as Hero's foundation,
was an instrument that produces a vertical
jet of water by air pressure.
Heron's Fountain