Why Do We Use Why Do We Use Coordinate Geometry?Coordinate Geometry?

Euclid’s Elements (about 300 B.C.)Euclid’s Elements (about 300 B.C.)

http://www.claymath.org/euclid/http://www.claymath.org/euclid/

Euclidean GeometryEuclidean Geometry

Euclid was a Greek Euclid was a Greek philosopherphilosopher(c. 330 BC to 275 BC)(c. 330 BC to 275 BC)

Euclidean geometry Euclidean geometry analyses shapes like analyses shapes like points, lines, and circlespoints, lines, and circles

These figures are These figures are described relative to one described relative to one anotheranother

There are no absolute There are no absolute locations (coordinates) locations (coordinates) and no algebraand no algebra

René DescartesRené Descartes

René Descartes (1596-1650) René Descartes (1596-1650) was a French philosopher, was a French philosopher, mathematician, scientist, and mathematician, scientist, and writerwriter

Called “The Founder of Called “The Founder of Modern Philosophy”Modern Philosophy”

Also called “The Father of Also called “The Father of Modern Mathematics”Modern Mathematics”

Cartesian CoordinatesCartesian Coordinates

Descartes used Descartes used algebra to describe algebra to describe points, lines, and points, lines, and circles geometrically circles geometrically using a coordinate using a coordinate systemsystem

y

x ExamplesPoint (-2, 1)Line y = x + 2Circle x2 + y2 = 100

3

1

2xy

Descartes and CalculusDescartes and Calculus

Isaac Newton’s (1643-Isaac Newton’s (1643-1727) invention of 1727) invention of the the calculuscalculus depended on depended on Cartesian coordinatesCartesian coordinates

Calculus is basically the Calculus is basically the description of changedescription of change

Example: For this Example: For this parabola parabola y y = = xx22, the slope , the slope of the tangent line at of the tangent line at any point P is any point P is y y = 2= 2xx

y = xy = x22

Implications of NewtonImplications of Newton

Descartes’, Newton, and others Descartes’, Newton, and others thought that the universe could be thought that the universe could be completely described with completely described with mathematicsmathematics

All are but parts of one All are but parts of one stupendous whole,stupendous whole,Whose body Nature is, Whose body Nature is, and God the souland God the soulAlexander Pope (1688-Alexander Pope (1688-1744)1744)

The Clockwork Universe TheoryThe Clockwork Universe Theory Supposed that God originally created Supposed that God originally created

the world by putting matter into the world by putting matter into motion according to certain lawsmotion according to certain laws

Time took care of the restTime took care of the rest Everything was matter in motionEverything was matter in motion

http://zebu.uoregon.edu/2003/hum399/lec10.html

A Broken ClockA Broken Clock

The Clockwork Universe unraveled in The Clockwork Universe unraveled in the 20the 20thth century century

The theory of quantum physics says The theory of quantum physics says that the universe consist of particles that the universe consist of particles that behave statistically like dice, not that behave statistically like dice, not predictably like a clockpredictably like a clock

Computer Models Use Coordinate Computer Models Use Coordinate GeometryGeometry

Computer models are widely used inComputer models are widely used in• engineeringengineering• computer gamescomputer games• computer musiccomputer music• astrophysicsastrophysics

Math HerosMath Heros

What’s a hero?What’s a hero?

What’s a math What’s a math hero?hero?

©Jen Sorensen

Math HerosMath Heros

Dr. Albert EinsteinDr. Albert Einstein(1879 - 1955)(1879 - 1955)

Dr. Stephen HawkingDr. Stephen Hawking(1942 - ) (1942 - )

Professor Lee LorchProfessor Lee Lorch

(1915 – present )(1915 – present )

Professor Lee LorchProfessor Lee Lorch Took real risks helping African American Took real risks helping African American

women get their PhD’s in mathematics women get their PhD’s in mathematics during the 1950’s and 1960’s during the 1950’s and 1960’s

Not a famous mathematicianNot 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