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The Beginning of Greek Mathmatics
Transcript of The Beginning of Greek Mathmatics
at 50 Pythagoreans , Pythagoras settled in Italy and started his own school.
"Quadrivium" - the fourfold division of knowledge.
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
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