# 1637

## Cartesian coordinates

## The book of science

Tom Sharp

Tom Sharp

René Descartes geometry |

- Algebra had nothing to do with geometry.
- Geometry had been conducted without numbers
- using only compass and straightedge, as Plato had taught.
- Numbers were for craftsmen and businessmen.
- But Pierre de Fermat showed that an equation
- could be described as a curve
- and René Descartes showed that a curve
- could be described by an equation.
- The work of Descartes was difficult and incomplete.
- Translated into Latin and explained, however,
- it correlated geometry and algebra
- and enabled the development of calculus.

- The beauty of x
^{2}+ y^{2}= 1 - the unit circle
- penetrated my befuddled head.
- How could high school seem so easy
- when I was barely aware
- of what I was doing there?
- The equations for line and circle
- the elegance of each solution
- encompassed me.

- A tribe in the South American rainforest
- has no word for left or right.
- Absolute directions are all they use.
- Instead of reading a page from left to right,
- they would need to orient the top of the page to the north
- for example, and read from west to east.
- The Mayans had one name for both blue and green
- although they could qualify a color to describe its hue, brightness,
- saturation, texture, pattern, translucence, wetness, and shape.
- Neither the
*Iliad*nor the*Odyssey*use a word for blue. - Ancient Greeks described the sky as bronze,
- but wouldn’t the sky for them have been a particular kind of bronze?
- Are our lives more complicated? More uncertain?
- Perturbations and chaos have always seemed to intervene
- when trying to fit the ideal to life’s curves.

Nicole Oresme and Pierre de Fermat independently invented two-dimensional and three-dimensional coordinate systems, but the publication by Descartes in 1637 had a huge influence, including facilitating the development of calculus by Newton and Leibniz. Descartes used only a single axis; commentators including Frans van Schooten added the second perpendicular axis.

See also in

The book of science:Geometry—EuclidNumber system—Leonardo Pisano Bigollo (Fibonacci)Readings on wikipedia:

Other readings: