Toshikazu Kawasaki
Encyclopedia
is a Japanese
paperfolder
and origami theorist
who is known for his geometrically innovative models. He is particularly famous for his series of fourfold symmetry "roses", all based on a twisting maneuver that allows the petals to seem to curl out from the center of the flower. Kawasaki also teaches Mathematics at Sasebo Technical Junior College.
Kawasaki is responsible for some very interesting theories, mathematically speaking. He 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. He also discovered and proved that with any given flat point in an origami model, the sum of alternating angles is always equal to 180 degrees, a result now known as Kawasaki's theorem
.
and Toshie Takahama, Origami for the Connoisseur. Japan Publications.
Japanese people
The are an ethnic group originating in the Japanese archipelago and are the predominant ethnic group of Japan. Worldwide, approximately 130 million people are of Japanese descent; of these, approximately 127 million are residents of Japan. People of Japanese ancestry who live in other countries...
paperfolder
Origami
is the traditional Japanese art of paper folding, which started in the 17th century AD at the latest and was popularized outside Japan in the mid-1900s. It has since then evolved into a modern art form...
and origami theorist
Mathematics of paper folding
The art of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability and the use of paper folds to solve mathematical equations.-Flat folding:The construction of origami models is sometimes shown as crease...
who is known for his geometrically innovative models. He is particularly famous for his series of fourfold symmetry "roses", all based on a twisting maneuver that allows the petals to seem to curl out from the center of the flower. Kawasaki also teaches Mathematics at Sasebo Technical Junior College.
Kawasaki is responsible for some very interesting theories, mathematically speaking. He 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
Crease pattern
A Crease Pattern is an origami diagram type that consists of all or most of the creases in the final model, rendered into one image. This comes in handy for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently.The use of crease patterns...
and then collapsing it to find a finished form, usually a geometric shape such as a cube. He also discovered and proved that with any given flat point in an origami model, the sum of alternating angles is always equal to 180 degrees, a result now known as Kawasaki's theorem
Kawasaki's theorem
Kawasaki's theorem is a theorem in the mathematics of paper folding, named after Toshikazu Kawasaki, that gives a criterion for determining whether a crease pattern with a single vertex may be folded to form a flat figure.- Statement of the theorem :...
.
Resources
Kunihiko KasaharaKunihiko Kasahara
is a Japanese origami master. He has made hundreds of models, from simple lion masks to complex modular origami, such as a small stellated dodecahedron. He does not specialize in what is known as "super complex origami", but rather he likes making simple, elegant animals, and modular designs such...
and Toshie Takahama, Origami for the Connoisseur. Japan Publications.