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Real Projective Plane

See antipodal identification through a Boy surface immersion.

S2 / (x ~ -x)

First, notice

Find two regions that look far apart in the drawing, then imagine identifying opposite points.

Then, experiment

Rotate before changing the twist; the projection is the first idea to inspect.

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 modelReal Projective Plane

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: Klein Bottle