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Why Do We Use Coordinate Geometry?. 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

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Euclid s elements about 300 b c
Euclid’s Elements (about 300 B.C.)

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


Euclidean geometry
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


Ren descartes
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
Cartesian Coordinates

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


Descartes and calculus
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
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
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
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 Use Coordinate Geometry

  • Computer models are widely used in

    • engineering

    • computer games

    • computer music

    • astrophysics


Math heros
Math Heros

  • What’s a hero?

  • What’s a math hero?

©Jen Sorensen


Math heros1
Math Heros

  • Dr. Albert Einstein(1879 - 1955)

  • Dr. Stephen Hawking(1942 - )

  • Professor Lee Lorch(1915 – present )


Professor lee lorch
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