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Why Do We Use Coordinate Geometry?PowerPoint Presentation

Why Do We Use Coordinate Geometry?

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Euclid’s Elements (about 300 B.C.)

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

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 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

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)

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

- 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

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