Imagine that the Earth was a geometric object, a sphere only slightly out of true. Well it is a geometric object, since after all, geo = earth. Trigonometry originated not in abstract numbers but in real measurements of real landscapes and landmarks. Everywhere I look on this planet, I am looking at trigonometry, with the right angles being those made by the downward pull of gravity, perpendicular to the surface of the Earth sphere. This is not Newtonian or even Galilean, it is much earlier, originating in antiquity with Babylonian triangles and Hellenistic plumb bobs.

If I wanted to use calculus I could claim that even though I am placed on a sphere with a curved surface, that point of perpendicularity (or a tangent, horizontally) is a moment of flatness. Gravity points down to a derivative that is a tiny piece of flat earth. Disregard those hills and valleys, the Earth is flat, at least where gravity puts its point.

Trigonometry places its measurements in a "unit circle," a universal circle whose radius is always ONE. If Earth is a unit circle, a perfect section of a sphere, does that mean that Earth is a unity? Utopians wish for Just One Earth where everyone lives in "harmony," a Pythagorean dream. But the measurement of radians insists that all circle circumferences and the angles that sector them are all some measure of Pi. Everywhere a circle goes, there goes Pi. Is it possible to have a circle whose circumference is a rational number? Perhaps it isn't. Earth will always be irrational, and its numbers will never end.

"Earth Unit Circle," acrylic on black-coated thick paper. 10" x 10"

Posted at 1:53 am | link