3 - Curves

Summary

Say you bounce a ball

Have you ever noticed that

Between the business of its going up

and the business of its fall

it hesitates?

It just waits There's a fraction of a second there

when it's luxuriating in the air

Before its fate rushes it on.

– from “Circe and the Hanged Man”, Ellen McLaughlin (2010)

Even if you sequester yourself in nature, away from the influences of humankind, the world moves in curious, patterned ways. Why does one falling leaf drift in a spiral while another twirls about its axis? What explains the eddy patterns in a creek? What forces act on a bird's wing? Why do the stars travel a circle during the night? Thinkers from many cultures looked beneath the surface of questions like these; underlying all of the answers was mathematics.

Oresme invents a precursor to a coordinate system

Most thinkers who discover something about how the universe works want to share their discoveries, and some created notation intended to streamline this communication. Chapter 7, for example, is in part devoted to explaining the symbols that we use today in calculus. Equally important in our story is the development of visual tools that, paired with sophisticated notation, not only facilitated the sharing of results but also sparked ideas that almost certainly would have otherwise remained out of reach. One such groundbreaking tool in mathematics is the coordinate system — a graphical way of picturing how two or more variables relate — with origins that reach back to medieval Europe.