Cartesian coordinates Analytic geometry Handedness Commentary

René Descartes geometry

Cartesian coordinates

• 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.

Analytic geometry

• The beauty of x² + y² = 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.

Handedness

• 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.