of Mathematics The Beginnings Greek Pythagoras' School

at 50 Pythagoreans , Pythagoras settled in Italy and started his own school.

"Quadrivium" - the fourfold division of knowledge.

arithemetica (arithmetic)

harmonica (music)

geometria (geometry)

astrologia (astronomy)

Student were bound by oath to not disclose to outsiders

five-point star ( ) was the sign that members of the brotherhood Greek Guy BY: Linsey Brian Summer Kenny 3.1 The Geometrical Discoveries of Thales Greek math was separate from daily life

Greek math vs. Babylonian and Egyptian math

Greeks learned just to know stuff, not for practical application Greeks Unified math

Made it more profound, rational, and abstract

Ex: Rad 2 Greeks "traveled" A LOT!

colonized coast and islands of Asia minor Linsey Brian Kenny Summer The Greek Miracle!

How fast, variety, and quality of achievements

How other cultures accepted Greek's ideas In ancient Societies, community activities were directed by the "educated elite". 3.2 Pythagorean Mathematics VS. Intro of Pythagoras

Born on the Aegean island Samos (580-569 B.C.)

Pythagoras and his students, Pythagoreans, studied numbers in abstract Pythagoreans Theories

Everything , physical and spiritual, has been assigned its allotted number and form

"Everything is a number"

"Knowledge is the greatest purification" Music provided by the Pythagoreans

Discovered that notes sounded by a vibrating string depended on the string's length Pythagoreans View on Astronomy

Planets were carried around the earth on a crystal sphere of it's own

Noise generated by their motion - each planet would have a certain tone according to the distance from the center

The whole system created a celestial harmony = "music of spheres" Cosmic Philosophy and Number Mysticism

Everything material and spiritual assigned a definite integer

1. Reason

2. Man

3. Woman

4. Justice

5. Marriage (2+3=Man+Woman)

6. Creation Successor of Pythagoras: Nicomachus

Represented numbers by letters with definite values

Wrote Introductio which became the leading textbook of the time Geography Thales of Miletus Greek Alphabet

450 B.C., Greeks adopted an alphabetic notion for representing numbers

first nine letters of the Greek alphabet = first nine integers

next nine letters = first nine integral notions of 10

last nine letters = first nine integrals multiples of 100 Circa 635-547 B.C. Pythagorean's Number System

Did not have number symbols, So they thought of numbers in a visual ways. (Dots in a geometric pattern)

Numbers classified as triangular, square, pentagonal, etc,

Numbers like this are called figurative, or polygonal numbers First of the Seven Sages of Greece "Know thyself" "How can you tell what is going on in the sky when you can't see what is lying at your feet?" Credited with: Angle inscribed in Semicircle is right. A Circle is bisected by its diameter Creation The base angles of an Isosceles triangle are equal. If 2 straight lines intersect, opposite angles are equal. The sides of similar triangles are proportional. 2 triangles are congruent if one side and 2 adjacent angles, respectively, are equal. (SAA) Father of Geometry OR the FIRST Mathematician Probably contributed deductive method to Geometry Indirectly measured height of Great Pyramid using shadows! h/h' = s/s' Determined how far a ship at sea is from shore Pythagoras' Death

Possibly perished in an inferno 2. Write each of the following numbers as the sum of three or fewer triangular numbers:

a)56 = 55 + 1

b) 69 = 66 + 3

c) 185 = 120 + 55 + 10

d) 287 = 176 + 10 + 1 Triangular Numbers: Example Problem

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# The Beginning of Greek Mathmatics

Math sucks... Our History of Math Presentation. It was loads of fun. Not really. Help us.

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