82 GREEK MATHEMATICS

GREEK MATHEMATICS INTRODUCTION   The beginnings of Greek mathematics originated from the 6th century BC to the 5th century AD The word mathematics comes from the Greek word μάθημα (mathema), meaning "subject of instruction“ PERIODS IN GREEK MATHEMATICS    FIRST – influenced by Pythagoras SECOND – Plato and his school THIRD – Alexandrian School flourished in Grecian Egypt and extended its influence to Sicily and Palestine GREEK NUMBERS    Greeks had a variety of different ways of writing down numbers Some Greeks used a system based on writing the first letter of the word for that number For number ten “Deka”, they would draw a D to mean 10 (a delta, in the Greek alphabet) Some other numbers in greek symbols    Because the Greeks had very clumsy ways of writing down numbers, they didn't like algebra They were more focused on geometry, and used geometric methods to solve problems that you might use algebra for They found it very hard to write down equations or number   Greek mathematicians were very interested in proving that certain mathematical ideas were true They spent a lot of time using geometry to prove that things were always true,even thoughpeople like Egyptians and Babylonians already knew that they were true most of the time away    Because the Greeks had very clumsy ways of writing down numbers, they didn't like algebra They were more focused on geometry, and used geometric methods to solve problems that you might use algebra for They found it very hard to write down equations or number MOST FAMOUS GREEK MATHEMATICIANS     Thales Pythagoras Anaxagoras Democritus     Aristotle Hipocrates Euclid Archimedes  For him the base of mathematics is logic, but the nature of mathematical relations is completely specified by postulates that dictates the physical experience HIPPOCRATES (grč Ἱπποκράτης )  Lived from 460 BC to 377 BC  an ancient Greek physician and was considered one of the most outstanding figures in the history of medicine HIPPOCRATUS PROBLEM  He proved that the lune bounded by the arcs labeled E and F in the figure has the same area as does triangle ABO EUCLID (grč Εὐκλείδης )     Born 300 BC pioneer of axiomatics in geometry His work Elements fundamental work in the field of Greek mathematics influenced the development of mathematics in the next 20 centuries ELEMENTS written about 300 B.C  textbook that includes number theory  the Euclidean algorithm for finding the greatest common divisor of two numbers   the first edition of the translation from Arabic into The axiomatic method The Elements begins with definitions and five postulates There are also axioms which Euclid calls 'common notions' These are not specific geometrical properties but rather general assumptions which allow mathematics to proceed as a deductive science For example: “Things which are equal to the same thing are equal to each other.”” Euclid's fifth postulate cannot be proven from others, though attempted by many people Euclid used only 1—4 for the first 28 propositions of the Elements, but was forced to invoke the parallel postulate on the 29th In 1823,Bolyai and Lobachevsky independently realized that entirely self-consistent "nonEuclidean geometries" could be created in which the parallel postulate did not hold Our world is non Euclidean Restate the fifth postulate: Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line Spherical geometry is just as real as Euclidean geometry, but the theorems and general results are very different There are quite a few results from Euclidean geometry that are completely false in spherical geometry (and vice versa) ARCHIMEDES (grč Ἀρχιμήδης)    mathematician and inventor born 287 BC in Syracuse founder of quantitative physics as a mathematician, advocate of logical processes  He determined approximate values of some irrational numbers 1351/780> >265/153 28/7> π >223/71   A sphere has 2/3 the volume and surface area of its circumscribing cylinder A sphere and cylinder were placed on the tomb of Archimedes at his request LITERATURA     Vladimir Devide: “Na izvorima matematike” Dadić Žarko: “Povijest ideja i metoda u matematici i fizici”; ŠK, 1992 http//www.ibilio.org/expo/vatican.exh ibit/exhibit/dmathematics/Greek_math.html http://www.historyforkids.org Authors: Ivana Pušić Dajana Rudić Ines Malić ... Greek mathematics originated from the 6th century BC to the 5th century AD The word mathematics comes from the Greek word μάθημα (mathema), meaning "subject of instruction“ PERIODS IN GREEK MATHEMATICS. .. and extended its influence to Sicily and Palestine GREEK NUMBERS    Greeks had a variety of different ways of writing down numbers Some Greeks used a system based on writing the first letter... ten “Deka”, they would draw a D to mean 10 (a delta, in the Greek alphabet) Some other numbers in greek symbols    Because the Greeks had very clumsy ways of writing down numbers, they didn't