agewmerhtoz mhdeiz eisitw Let no one ignorant of

agewmerhtoz mhdeiz eisitw

“Let no one ignorant of geometry enter here “ - Plato

Lecture 01 S

1. Traditional Liberal Arts: Quadrivium - astronomy, arithmetic, geometry, and music; Trivium - logic, rhetoric, and grammar 1. 2. Geometry and its descendant, trigonometry, are essential tools in engineering, architecture, navigation, and other disciplines. 1. 3. We can learn how to draw valid conclusions from hypotheses and how to detect and avoid invalid reasoning. 1. 4. Geometry is also beautiful, and some of its theorems are so amazing as to seem almost miraculous.

Geometries • • • Euclidean Geometry Computational/Algorithmic Geometry Affine Geometry Inversive Geometry Projective Geometry Fractal Geometry Finite Geometry Non-Euclidean Geometry Descriptive Geometry Analytical Geometry Differential Geometry Topology • • •

The Three Rivers Civilizations

The Three Rivers Civilizations

River Civilizations

Gougu Theorem While it is not known as to on what basis Pythagoras derived this theorem, this ancient Chinese proof clearly shows that the people in the ancient east were very much aware of this theorem well before Pythagoras. (In fact, the earliest known proof of this theorem was provided by the ancient Indian Vedic mathematicians, more than 2000 years before Pythagoras. ) 1000 B. C. E.

Egypt ( Jean-Francois Champollion )

Egypt - from the Moscow Papyrus

Egypt - the Rhind Papyrus http: //en. wikipedia. org/wiki/Rhind_Mathematical_Papyrus

Babylon http: //en. wikipedia. org/wiki/Plimpton_322 Theorem: All primitive Pythagorean triples < a, b, d > are given by

India “ string - rules “ http: //en. wikipedia. org/wiki/Shulba_Sutras

agewmerhtoz mhdeiz eisitw “ Let no one ignorant of geometry enter here “ - Plato

The Pythagorean Theorem