1. Why Do We Use Coordinate Geometry?

2. Euclid’s Elements (about 300 B.C.)
This manuscript, dating from the year 888 AD, was copied by Stephen the Clerk in Constantinople, and since 1804 has been in the collection of the Bodleian Library.

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 ( ) 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 ( ) invention of the calculus depended 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 soul Alexander Pope ( )

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

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 ( )
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