Why Do We Use Coordinate Geometry?

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

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

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”

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

Descartes and Calculus Isaac Newton’s (1643-1727) 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

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 (1688-1744)

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

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

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

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

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

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