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There are two traditional methods for making polyhedra out of paper: polyhedral nets and modular origami.In the net method, the faces of the polyhedron are placed to form an irregular shape on a flat sheet of paper, with some of these faces connected to each other within this shape; it is cut out and folded into the shape of the polyhedron, and the remaining pairs of faces are attached together.
The Huzita–Justin axioms or Huzita–Hatori axioms are a set of rules related to the mathematical principles of origami, describing the operations that can be made when folding a piece of paper. The axioms assume that the operations are completed on a plane (i.e. a perfect piece of paper), and that all folds are linear.
Masahiro Chatani was a Japanese architect (certified, first class) and professor considered to be the creator of origamic architecture. From its development until his death in 2008, he was widely acknowledged to be the world's foremost origamic architect.
Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger [ de ] and published by Arbelos Publishing (Shipley, UK) in 2008.
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Origami tessellation is a branch that has grown in popularity after 2000. A tessellation is a collection of figures filling a plane with no gaps or overlaps. In origami tessellations, pleats are used to connect molecules such as twist folds together in a repeating fashion.
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Modular origami or unit origami is a multi-stage paper folding technique in which several, or sometimes many, sheets of paper are first folded into individual modules or units and then assembled into an integrated flat shape or three-dimensional structure, usually by inserting flaps into pockets created by the folding process. [3]