Mathematics · 34 visual lessons

Curves and spatial geometry
Change you can see.

Explore integration, differential equations, series, and geometry through physical models.

Follow the real situation, derive the mathematics, and test it with interactive graphs and worked practice.

Unit progressLoading progress…

Reading your saved completion. Completion is saved on this browser.

Unit 5 · 7 lessons

Curves and spatial geometry

An orbit can pass through vertical tangents and loop back in x. A parameter records both coordinates without forcing y to be single-valued in x.

A cardioid is easier to describe by distance and direction from a pole. Sweep its angle and watch the enclosed region grow.

A displacement has both length and direction. Change its components and follow the arrow and its magnitude.

A particle path can be described by a starting point plus a scaled direction vector. Its parameter controls position along the line.

Pushing sideways can exert a force without doing work along the displacement. Rotate the force to see the signed result.

A wrench is most effective when the force is perpendicular to its handle. Compare that with force along the handle.

A plane can be described by points whose displacement from a reference point is perpendicular to one normal vector.