How the coordinate plane makes calculus make sense Descartes did not invent calculus, but his coordinate plane made it intelligible. By giving functions a geometric home, it allowed change and accumulation to be seen rather than imagined. Derivatives grow naturally out of slope. What begins as the rise over run of a line becomes the slope of a curve at a point, visible as a tangent line. Rates of change stop being abstract symbols and become geometric objects. Integrals grow just as naturally ou