The geometric principle of paper cup fans is a classic embodiment of the design philosophy of "from plane to surface", and its application goes far beyond paper cups.

Rolling a fan-shaped piece into a cone is a simple "folding" action. A more advanced application is "origami engineering".

• Expandable structure: The solar panel of the satellite and the light shield of the space telescope are tightly folded during launch and unfolded according to a predetermined program after entering orbit. One of its core design ideas is to accurately "map" three-dimensional structures onto two-dimensional planes and design folding lines (like the boundaries of a sector), which is in line with the design logic of a sector.
• Medical stent: Some vascular stents are cut from a metal tube by laser, and their initial shape can be seen as a complex "mesh fan-shaped plate". After being delivered to the designated location of the blood vessel through a catheter, the balloon is expanded to support the vessel in a designed cylindrical shape.