1. Why Do We Use Coordinate Geometry?

2. Euclid’s Elements (about 300 B.C.) http://www.claymath.org/euclid/

3. Euclidean Geometry • Euclid was a Greek philosopher(c. 330 BC to 275 BC) • Euclidean geometry analyses shapes like points, lines, and circles • These figures are described relative to one another • There are no absolute locations (coordinates) and no algebra

4. René Descartes • René Descartes (1596-1650) was a French philosopher, mathematician, scientist, and writer • Called “The Founder of Modern Philosophy” • Also called “The Father of Modern Mathematics”

5. Cartesian Coordinates Descartes used algebra to describe points, lines, and circles geometrically using a coordinate system

6. Descartes and Calculus • Isaac Newton’s (1643-1727) invention of the calculusdepended on Cartesian coordinates • Calculus is basically the description of change • Example: For this parabola y = x2, the slope of the tangent line at any point P is y = 2x y = x2

7. Implications of Newton • Descartes’, Newton, and others thought that the universe could be completely described with mathematics • All are but parts of one stupendous whole,Whose body Nature is, and God the soulAlexander Pope (1688-1744)

8. The Clockwork Universe Theory • Supposed that God originally created the world by putting matter into motion according to certain laws • Time took care of the rest • Everything was matter in motion http://zebu.uoregon.edu/2003/hum399/lec10.html

9. A Broken Clock • The Clockwork Universe unraveled in the 20th century • The theory of quantum physics says that the universe consist of particles that behave statistically like dice, not predictably like a clock

10. Computer Models Use Coordinate Geometry • Computer models are widely used in • engineering • computer games • computer music • astrophysics

11. Math Heros • What’s a hero? • What’s a math hero? ©Jen Sorensen

12. Math Heros • Dr. Albert Einstein(1879 - 1955) • Dr. Stephen Hawking(1942 - ) • Professor Lee Lorch(1915 – present )

13. Professor Lee Lorch • Took real risks helping African American women get their PhD’s in mathematics during the 1950’s and 1960’s • Not a famous mathematician ..at 91, this gentle scholar can recall every racist rule he ever tackled: the "No-Negroes" housing complex where he pushed to have blacks made welcome; the all-white math conferences to which he insisted on bringing black professors; the all-black grade school where he tried to enroll his daughter….These fights lost him a string of jobs and in time got him blacklisted altogether for the "un-American" activity of championing racial equality, driving him to leave his homeland for Canada where he was in fierce demand as a math whiz. The Toronto Star, Jan 15, 2007