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.
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.
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.
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