← All models Connect the ideas

Closed Curves

Trace homotopy classes and holonomy around compact surfaces.

loops, winding, transport

First, notice

Compare the paths: which loops can be continuously reshaped into one another?

Then, experiment

Pause the motion to compare the paths one at a time.

Twist 0.65 Changes the parameter used to draw the model. Detail 64 Lower detail makes the construction easier to inspect. Show construction linesReveal the grid used to render the surface.

Live modelClosed Curves

Drag to rotateScroll to zoom

Initializing geometry...

Bright path = a route to trace Grid = construction lines

Make the connection

What changed when you moved one control?

Describe the change before naming it. That habit is the bridge from a visual model to mathematical language.

Next: Crosscap Particles