Early Greek Mathematics

1
Early Greek Mathematics

• MATH 4620/5620
• FA-04

2
The Greeks

• Made mathematics into one discipline giving it
  order, more abstraction, and development of
  knowledge for its own sake.
• Early documents are scarce so is difficult to
  gain a clear picture of Greek mathematics.
• No papyrus, no clay tablets so deduce it was
  books which did not stand the test of time.

3
The Greeks (cont.)

• As a consequence, most early Greek mathematics is
  a modge-podge of myths, legends, and anecdotes
  preserved by writers centuries later.
• This brings up the point of mistakes in copying,
  miscommunication, and individuals own
  perceptions of an event.

4
Greeks and travel

• The Greeks were great travelers
• All early Greek mathematics came from the
  outposts in Asia Minor, southern Italy, and
  Africa (not mainland Greece).
• Development of writing and the alphabet with
  both consonants and vowels (400 B.C.)
• Coinage in precious metals was invented in the
  Greek cities of Asia Minor (700 B.C.)

5
Education

• Greek education was more broadly based and
  designed to produce gentleman amateurs.
• The Greeks had no powerful priesthood that could
  monopolize learning the educated came from
  people of affairs for whom business was a
  profession and learning a pastime.

6
Some history

• Hard to have a single ruler since spread out
  unlike Egyptians and Babylonians.
• Alexander the Great unified Greece and carried
  the civilization to great bounds typically
  called the Hellenistic Age.
• Rise of Greek mathematics coincides in time with
  the progress of Greek civilization in sixth
  century B.C.

7
Whos who in Mathematics?

• Almost all the really productive work was done in
  the short interval from 350 to 200 B.C.
• The early mathematicians Thales of Miletus
  (625-547 B.C.), Pythagoras of Samos (580-500
  B.C.)
• Euclid, Archimedes, and Apollonius came later
  along with Ptolemy, Pappus, Diophantus.

8
THALES The father of geometry

• Shrewd in politics and commerce
• Skilled in astronomy
• Generally considered to be the first to introduce
  logical proof based on deductive reasoning rather
  than experimentation and intuition.

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Geometric Propositions

• An angle inscribed in a semicircle is a right
  angle.
• A circle is bisected by its diameter.
• The base angles of an isosceles triangle are
  equal.
• If 2 straight lines intersect, the opposite
  angles are equal.
• The sides of similar triangles are proportional.
• Two triangles are congruent if they have one side
  and two adjacent angles, respectively, equal.
• NOTE Beginning of the development of geometry.

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Thales use of geometry

• Indirect measurement of the height of the Great
  Pyramid by means of shadows
• How far a ship at sea is from the shore