2. The Mathematics that we know in the modern world has its roots in ancient
Mesopotamia, Egypt and Babylonia. Then it was developed in Greece, and
simultaneously in China and in India. This ancient Greek mathematics, along
with some influence of Hindu mathematics spread to the neighboring countries
in the Middle East. It was translated into Arabic and Latin and was adopted by
Western Europe. Western education was spread throughout the world by
colonization and trade. Today’s Mathematics has been enriched by the
contributions of different civilizations and individual mathematicians who
unselfishly passed on their discoveries and knowledge to us. It is therefore
fitting for us to look back and appreciate how Mathematics have developed
and who made these developments possible.
Overview/Introduction:
3. A. Number Systems and Arithmetic
• Development of numeration systems.
• Creation of arithmetic techniques, lookup tables, the abacus and other
calculation tools.
B. Practical Measurement, Geometry and Astronomy
• Measurement units devised to quantify distance, area, volume, and
time.
• Geometric reasoning used to measure distances indirectly.
• Calendars invented to predict seasons, astronomical events.
• Geometrical forms and patterns appear in art and architecture.
Ancient Period (3000 B.C. to 260 A.D.)
4. Practical Mathematics
As ancient civilizations developed, the
need for practical mathematics
increased. They required numeration
systems and arithmetic techniques for
trade, measurement strategies for
construction, and astronomical
calculations to track the seasons and
cosmic cycles.
5. Babylonian Numerals
The Babylonian Tablet Plimpton 322
This mathematical tablet was recovered from an unknown place in the Iraqi
desert. It was written originally sometime around 1800 BC. The tablet
presents a list of Pythagorean triples written in Babylonian numerals. This
numeration system uses only two symbols and a base of sixty.
6. Chinese Mathematics
Diagram from Chiu Chang
Suan Shu, an ancient Chinese
mathematical text from the
Han Dynasty (206 B.C. to A.D.
220).
This book consists of nine
chapters of mathematical
problems. Three involve
surveying and engineering
formulas, three are devoted to
problems of taxation and
bureaucratic administration,
and the remaining three to
specific computational
techniques. Demonstration of the Gou-Gu
(Pythagorean) Theorem
8. A. Greek Logic and Philosophy
• Greek philosophers promote logical, rational explanations of
natural phenomena.
• Schools of logic, science and mathematics are established.
• Mathematics is viewed as more than a tool to solve practical
problems; it is seen as a means to understand divine laws.
• Mathematicians achieve fame, are valued for their work.
B. Euclidean Geometry
• The first mathematical system based on postulates, theorems and
proofs appears in Euclid's Elements.
Greek Period (600 B.C. to 450 A.D.)
9. Area of Greek Influence
Archimedes of
Syracuse
Euclid and Ptolemy of
Alexandria
Pythagoras of
Crotona
Apollonius of
Perga
Eratosthenes of
Cyrene
10. Mathematics and Greek Philosophy
Greek philosophers viewed the universe in mathematical terms.
Plato described five elements that form the world and related
them to the five regular polyhedra.
11. Euclid’s Elements
Greek, c. 800 Arabic, c. 1250 Latin, c. 1120
French, c. 1564 English, c. 1570 Chinese, c. 1607
Translations of Euclid’s Elements of Gemetry:
The Pythagorean Theorem
14. Archimedes Screw
Archimedes’ screw is a mechanical device used to lift water and such light
materials as grain or sand. To pump water from a river, for example, the
lower end is placed in the river and water rises up the spiral threads of the
screw as it is revolved.
