Sardinia

In 1860, Vittorio Emanuele II, King of Sardinia became also the first King of Italy after conquering the rest of the peninsula. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures. In 1792, Jean-Paul Marat, son of a Sardinian father from Cagliari and a Swiss mother, was one of the triumvirate leading the French Revolution. Once this figure is computed, the creases which are then used to obtain the base structure can be added. In 1718 Sardinia became an independent kingdom under the House of Savoy, rulers of Piedmont. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. This was the first time Turks lost out to Europeans signaling a trend of military decline and defeats from which Turks never recovered. For a specific class of origami bases known as 'uniaxial bases', the pattern of allocations is referred to as the 'circle-packing'.

The sight of the admiral's head on a spear put such a fear in the heart of the Turks, that they abandoned the fight and completely surrendered to Christians. Rather, what is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. On October 7, 1571, at the Battle of Lepanto, Sardinian mariners on Board the admiralship of Infante Don John of Austria, half brother of Felipe II, boarded the Turkish admiralship, overpowered the crew, and cut off the head of a Turkish admiral. Paradoxically enough, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the crease pattern. Under Spain, Sardinians were regularly employed on the royal Spanish fleet. Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams. After the merge of the Kingdoms of Castile and Aragon, Sardinia was incorporated into the newly created national entity, Spain. The main starting point for such technical designs is the crease pattern (often abbreviated as 'CP'), which is essentially the layout of the creases required to form the final model.

The native population of the city of Alghero (S'Alighera in Sardinian, L'Alguer in Catalan) was expelled and the city repopulated by the Catalan invaders, whose descendants spoke Catalan till quite recently. This method of origami design was pioneered by Robert Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with full complement of fingers and toes, and the like. In 1323, the Kingdom of Aragon began a campaign to conquer Sardinia; the giudicato of Arborea successfully resisted this and for a time came to control nearly the entire island, but its last ruler Eleanor of Arborea, was eventually defeated by the Aragonese in the decisive Battle of Sanluri, June 30, 1409. With advances in origami mathematics however, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs. At various times, these fell under the sway of Genoa and Pisa. In the early days of origami, development of new designs was largely a mix of trial-and-error, luck and serendipidity. By 900, these districts had become four independent constitutional monarchies. Technical origami, also known as origami sekkei, is a field of origami that has developed almost hand-in-hand with the field of mathematical origami.

To provide for local defense, he divided the island into four Giudicati, Gallura, Logudoro, Arborea, and Caralis. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites. Especially after the conquering of Sicily in 832, the Byzantines were unable to effectively defend their most distant province, and the provincial judge assumed independent authority. The problem of rigid origami ("if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we still fold the model?") has great practical importance. Beginning in the eighth century, Arabs and Berbers began raiding Sardinia. [1]. Byzantine rule was practically nonexistent in the mountainous Barbagia region in the eastern part of the island, and an independent kingdom persisted there from the sixth through ninth centuries. Folding a flat model from a crease pattern has been proven by Marshall Bern and Barry Hayes to be NP complete.

Under the Byzantines, the imperial representative was a judge who governed from the southern city of Caralis. For instance, the problem of flat-foldability (whether a crease pattern can be folded into a 2-Dimensional model) has been a topic of considerable mathematical study. From 456 - 534, Sardinia was a part of the short-lived kingdom of the Vandals in North Africa, until reconquered by the Byzantine emperor Justinian I. The practice and study of origami encapsulates several subjects of mathematical interest. In 238 BC, after being defeated by the Roman Republic during the First Punic War, Carthage ceded Sardinia to Rome. Also, these papers are extremely thin and compressible, allowing for thin, narrowed limbs as in the case of insect models. The settlers called for help from Carthage, and the island became a province in the Carthaginian Empire. As these papers are floppy to start with, they are often backcoated or resized with methylcellulose or wheat paste before folding.

In 509 BC, war broke out between the native Nuragic people and the Phoenician settlers. Artisan papers such as unryu, lokta, hanji, gampi, kozo, saa have long fibres and are often extremely strong. Beginning around 1000 BC, Phoenician mariners established several ports of trade on the Sardinian coast. Both types of foil materials are suitable for complex models. The density, extensiveness and sheer size of the architectural remains from the Neolithic period, points to a considerable population of the island. Foil-backed paper is available commercially but not tissue foil. Genetics has now shown that Sardinians are a pre-Indo-European population and, like Basque, different from all surrounding and much younger groups. A second piece of tissue can be glued onto the reverse side to produce a tissue/foil/tissue sandwich.

However most theories regarding the original population of Sardinia have been formulated prior to genetics research and in the traditional frame of east-west movements. Related to this is tissue foil, which is made by gluing a thin piece of tissue to kitchen aluminium foil. According to some linguistic studies, the town of Sardis in (Lydia) would have been their starting point from which they would have reached the Tyrrhenian Sea, dividing into what were to become the Sardinians and the Etruscans. Foil-backed paper, just as its name implies, is a sheet of thin foil adhered to a sheet of thin paper. This assertion holds some truth; in fact most of the tombe dei giganti have a tombstone shaped like a ship vertically dug into the ground, bearing witness to their sea traveling activities. The weight of kami is slightly less than that of copy paper, making it suitable for a wider range of models. Shardana and Shekelesh were also called by the Egyptians as the "people from the faraway islands", implying that Shardana were already residents of Sardinia at the time of the Egyptian expedition. It is commonly coloured on one side and white on the other; however, duo coloured kami and patterned kami exist and can be used effectively for colour-changed models.

Shardana had joined the Shekelesh and others to form the coalition of the Sea Peoples, but were defeated by Ramses III around 1180 BC in Egypt. Kami is sold in prepackaged squares of various sizes ranging from 2.5 cm to 25 cm or more. It is speculated that, among others, the Shardana people landed in Sardinia coming from the eastern Mediterranean. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when dry. Still today, more than 9,000 Nuraghe survive. Heavier weight papers of 100 gsm or more can be wetfolded. From Neolithic times till the Roman Empire, the Nuragic civilisation took shape on the island. Normal copy paper with weights of 70–90 gsm can be used for simple folds, such as the crane and waterbomb.

The Cannonau wine is made with these grapes and may qualify as the mother of all the European wines. Although almost any laminar material can be used for folding, the choice of material used greatly affects the folding and final look of the model. Desiccated grapes, recently found in several locations, were DNA tested and proved to be the oldest grapes in the world, dating back to the Pyramids' and Mesopotamia’s era. A list of techniques is accumulating in the origami tech tree. In Prehistory Sardinia's inhabitants developed a trade in obsidian, a stone used for the production of the first rough tools, and this activity brought Sardinians into contact with most of the Mediterranean people. Most origami folds can be broken down into simpler steps. In 1979 human remains were found that were dated to 150,000 BCE. Influenced by the purity and beauty of Origami, and Japanese design principles, Orikaso processes can be used to create functional and useful products.

Sardinia's history is very ancient. Taking Origami developments into the 21st Century, designer Jay Cousins created a simpler form of Origami in plastic - dubbed orikaso. It lacks many species instead, like the viper and the marmot, which are found everywhere else on the continent. In one version, Sadako wrote a haiku that translates into English as:. Sardinia is a precious natural resource, containing thousands of rare or uncommon animals and plant species such as the Mediterranean Monk Seal and the boar. The tale of Sadako has been dramatized in many books and movies. It is highly recommended to make the trip from Macomer to Bosa Marina, where the train winds its way through the typical Sardinian landscape to reach the sea near the coastal town of Bosa situated in the west of the island. A group of one thousand paper cranes is called senbazuru in Japanese.

The train connects Cagliari to Arbatax in the south and Sassari to Palau in the north. Every year the statue is adorned with thousands of wreaths of a thousand origami cranes. It is slow but it allows the traveller to have scenic views impossible to see from the main road. While her effort could not extend her life, it moved her friends to make a granite statue of Sadako in the Hiroshima Peace Park: a young girl standing with her hand outstretched, a paper crane flying from her fingertips. Many tourists catch the trenino verde which runs through the wildest parts of the island. Sadako was buried with a wreath of 1,000 cranes. Some run on narrow gauge track. Her classmates continued folding cranes in honor of their friend.

Trains on Sardinia connect the whole island but are rather slow. Sadako folded 644 cranes before she died. The Sardinian economy is today focused on tourism (peaking with the Costa Smeralda), industry, commerce, services and information technology; an increasing income is coming from its famous wines and gastronomy. It is said that what made the girl truly special in her effort was her additional wish to end all such suffering, to bring peace and healing to the victims of the world. Several gold and silver mines operate on the island. However, it was not just for herself that she wished healing. "Unu Francu", referring to the now long-gone money, is a term used by older natives to mean some small amount, much as in English "It's not worth the price". Hearing the legend, she decided to fold 1,000 cranes so that she could live.

"su Pidzu"); 1 francu = 1,000 former Italian lire. By the time she was twelve in 1955, she was dying of leukemia. Sardinia's currency (as a part of Italy) is now the Euro, but in some rural areas Sardinians and towns, above all Cagliari, still unofficially refer to su Francu (or loc. She was then, a hibakusha -- an atom bomb survivor. In the city of Alghero in the north, a Medieval dialect of Catalan is still spoken (the name of the city in Catalan is L'Alguer) as the island was an Aragonese colony in the past. Sadako was exposed to the radiation of the atomic bombing of Hiroshima as an infant, and it took its inevitable toll on her health. In the island of San Pietro, the dialect spoken is a mix of Sardinian and Italian language coming from Liguria Genoa. The origami crane (折鶴 orizuru in Japanese) has become a symbol of peace because of this legend, and because of a young Japanese girl named Sadako Sasaki.

The spoken language was spread by the first settlers to Corsica, giving then origin to a new variety of language Sardinian-Corsican language. Legend says that anyone who folds one thousand paper cranes will have their heart's desire come true. In the northern regions of Gallura and Sassari, tatarese is spoken. Japan has launched a satellite named tsuru (crane). While it has been significantly supplanted by Italian for official purposes, Sardinian is still widely spoken in rural areas. The crane is auspicious in Japanese culture. The most spoken languages in Sardinia are Italian and Sardinian, a Romance language of Latin origin, but with an obscure Pre-Roman element, including Phoenician, Etruscan, and Near Eastern languages. One of the most famous origami designs is the Japanese crane.

The climate is mainly Mediterranean, with a warm spring and fall, hot summer, and mild winter. The model, contrary to common theory of traditional origami, involved cutting and gluing. See also: Tourist destinations of Sardinia. Masao Okamura, an origami historian, was able to recreate the model. The island is particularly famous for its beaches, but is also rich in other interesting places. A three volume wood cut book, "Ranma-Zushiki", published in 1734, contained two pictures that were identified by Yasuo Koyanagi in 1993 as the Tamatebako model. The island contains numerous extraordinary tourist areas, including the Costa Smeralda and Gennargentu. Recent historians have uncovered the lost origami Tamatebako, a model from the folk tale of "Urashima-Taro and the Tamatebako".

The other region is Veneto. Modern origami has attracted a worldwide following, with ever more intricate designs and new techniques such as 'wet-folding,' the practice of dampening the paper somewhat during folding to allow the finished product to hold shape better, and variations such as modular origami also known as unit origami, where many origami units are assembled to form an often decorative whole. a distinct people) by the Italian Parliament. His work was promoted through the studies of Gershon Legman as published in the seminal books of Robert Harbin Paper Magic and more so in Secrets of the Origami Masters which revealed the wide world of paperfolding in the mid 1960s. Sardinia is one of two Italian regions whose inhabitants have been recognised as a "popolo" (i.e. The work of Akira Yoshizawa of Japan, a prolific creator of origami designs and writer of books on origami, inspired a modern renaissance of the craft. See also: Sardinian towns. Friedrich Fröbel, founder of the kindergartens, recognized paper binding, weaving, folding, and cutting as teaching aids for child development during the early 1800s.

The region is divided into eight provinces: Cagliari, Sassari, Nuoro, Oristano, Olbia-Tempio, Ogliastra, Carbonia-Iglesias and Medio Campidano. His methods, which involved sheets of round paper that were folded into spirals and curved shapes, have influenced modern origami artists like Kunihiko Kasahara. The regional capital is Cagliari. Joseph Albers, the father of modern color theory and minimalistic art, taught origami and paper folding in the 1920s and 30s. Sardinia is an autonomous region of Italy. The Japanese do not see origami as an art form, but rather as an integrated part of their culture and tradition. Sardinia has an area of 24,090 km² and a population of 1.65 million. Modern origami has broken free from the traditional linear construction techniques of the past, and models are now frequently wet-folded or constructed from materials other than paper and foil.

. Sometimes the most complex origami models must be folded from foil instead of paper; this allows more layers before the paper becomes impractically thick. Last and present name has been Sardinia, for the Shardana (who also had been expelled in Egypt by Ramses III circa 1180 BC). An origami design can be as simple as a party hat or paper airplane, or as complex as a model of the Eiffel Tower, a leaping gazelle or a stegosaurus that takes an hour and a half to fold. Sandalyon was its second name, probably due to its shape, recalling a footprint. The earliest known European origami is probably the baptismal certificate of 16th century, represented by a little bird (pajarita in Spanish or cocotte in French). At the beginning of the nuragic age circa 1500 BC the island was first called Hyknusa (latinized Ichnusa) by the Greeks probably meaning island (nusa) of the Hyksos, the people who had just been expelled by Ahmose I of Egypt circa 1540 BC and were by now looking for a new home. In Korea, ancestral tablets made of paper, known as jibang (지방), were folded in a prescribed manner handed down the family line for use in ancestral worship ceremonies.

It forms part of Italy. The earliest known Japanese origami is probably ceremonial paper folding, such as noshi (熨斗), which started in Muromachi era (1392-1573). Sardinia (Sardegna in Italian, Sardigna, Sardinna or Sardinnia in the Sardinian language, Sardenya in Catalan), is the second largest island in the Mediterranean Sea (Sicily is the largest), between Italy, Spain and Tunisia, south of Corsica. The earliest known traditions of paper folding were of ritual origin. This cheese is called Casu Marzu. The "invention" of paper folding probably followed soon after the invention of paper itself. Cheese filled with live maggots and their feces is a delicacy in Sardinia. .

The last four are new provinces since May 2005. It's also possible to create folds from triangular paper. Contrary to most popular belief, traditional Japanese origami, which has been practiced since the Edo era (1603-1867), has often been less strict about these conventions, sometimes cutting the paper during the creation of the design (Kirigami 切り紙) or starting with a rectangular, circular, or other non-square sheets of paper. In general, these designs begin with a square sheet of paper, whose sides may be different colors, and proceed without cutting the paper. Origami only uses a small number of different folds, but they can be combined in a variety of ways to make intricate designs.

The word literally means "paper folding" in Japanese and refers to all types of paper folding, even those of non-Japanese origin. The goal of this art is to create a given result using geometric folds and crease patterns.
Origami (折り紙 or 折紙 origami "paper folding") is the art of paper folding.