There are a few underlying ideas to run through before getting to the more complex aspects of this branch of mathematics.
- Folding involves geometrically transforming a flat sheet of material
- When you fold a flat sheet, an edge is created, which acts as a hinge that can move freely
- A vertex occurs when two or more edges meet at a point
- A crease pattern is fundamentally a graph that has been embedded within a bounded plane, containing edges and vertices
We must make some assumptions when using these principles to design structures:
- The material used is inextensible – it doesn’t stretch; all distances remain the same
- The panels created are rigid – areas between creases do not bend smoothly; they act as stiff plates
- Creases act as hinges – freely moving so the sheet can rotate about these edges
- Thickness is ignored at first – treat the sheet as having ‘zero thickness’ to mathematically model it
These assumptions allow civil engineers to most efficiently model how something will behave before transferring the design into the real world.