The Topology of the Fitted Sheet

From Chaos to Rectangle

Part 1: The Problem

The "Bag" State

A flat sheet is a 2D plane. A fitted sheet, however, is topologically distinct because of its elastic corners. It behaves like a 3D "bag."

If you try to fold it like a piece of paper, the elastic resists.

Standard algorithms fail on non-planar geometry.

Part 2: The Transformation

The "Hammock" Setup

To solve this, we must transform the 3D "bag" into a 2D rectangle. We do this by mapping the corners on top of each other to neutralize the curvature.

Interact: Drag the slider to fold the Right Side (C & D) all the way onto the Left Side (A & B).

A B Left Side
C D Right Side
Aligned

Once aligned, the sheet enters the "Salsa Skirt" state: a long, flat rectangle. The geometry problem is solved.

Part 3: Recursive Reduction

The Math of Folding

Now it is merely an area reduction problem. We apply a recursive function: Area_new = Area_current / 2.

Area = 100%
Salsa Skirt