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In 1893, Indian civil servant T. Sundara Row published Geometric Exercises in Paper Folding which used paper folding to demonstrate proofs of geometrical constructions. This work was inspired by the use of origami in the kindergarten system. Row demonstrated an approximate trisection of angles and implied construction of a cube root was ...
Kawasaki was the first to develop the technique of iso-area folding, which allows the folder to end up with each side of the paper displayed in equal amounts. It consists of building a mirror-symmetrical crease pattern and then collapsing it to find a finished form, usually a geometric shape such as a cube.
Cut a diagonal X across the entire center square, pinwheel-fold the outer edges, and fold the protruding pinwheel flaps inward, interleaving them to produce a multilayered square with the top woven together. Fold outward the triangular flaps cut from the center square. This creates one face of the cube; the entire cube requires six identical ...
Folding a Sonobe module (1–10) and assembly into a pyramid (11–12); * denote tabs and # denote pockets [10] Each individual unit is folded from a square sheet of paper, of which only one face is visible in the finished module; many ornamented variants of the plain Sonobe unit that expose both sides of the paper have been designed.
16th-century horoscope of archbishop John Hamilton, cast by Gerolamo Cardano, with lines resembling the fold lines of a paper fortune teller. Certain horoscopes from as far back as 12th-century Spain have a layout resembling this fold pattern, but they are not known to have been folded, nor to have been used in the same way as a paper fortune ...
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]
Strip folding is a combination of paper folding and paper weaving. [30] A common example of strip folding is called the Lucky Star, also called Chinese lucky star, dream star, wishing star, or simply origami star. Another common fold is the Moravian Star which is made by strip folding in 3-dimensional design to include 16 spikes. [30]
For rigid origami (a type of folding that keeps the surface flat except at its folds, suitable for hinged panels of rigid material rather than flexible paper), the condition of Kawasaki's theorem turns out to be sufficient for a single-vertex crease pattern to move from an unfolded state to a flat-folded state.
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