One knob makes a curve. Two knobs make a world.

Parametric modeling and multivariable calculus, in a nutshell, as ten live examples that build on each other: a point driven by one parameter becomes a curve, a Bézier spline — the modeling tool behind CAD — a mountain whose gradient and partial derivatives you can slice, a torus and a Möbius strip, a pipe swept along a curve the way a CAD kernel builds a solid, and finally volume under a surface and the butterfly curve. Every example carries the exact formula to paste into Desmos or GeoGebra, a presenter line, and a calculus hook. Even the ARTEMIS Academy wordmark at the top of the lesson is drawn by the subject itself: a Fourier series of rotating vectors tracing the letters.

Lesson

Parametric Modeling · Multivariable Calculus · 10 interactive examples

Platform

Interactive presentation · Desmos 2D/3D + GeoGebra 3D formulas

Rendering

Occlusion + light modes · adopted from the credited Desmos 3D graphers