

Humiaki Huzita I was greatly saddened to hear of the death of Humiaki Huzita or Humi as he was always known and especially on hearing from Roberto Morassi that he died following a car crash. I last met Humi (as I shall always know him) at the CDO convention at Florence in 2004, when he was his usual cheerful self. I have been becoming increasingly aware of Humi’s importance in the history of Origami. Apart from his contributions to the mathematics of origami he was generally unknown outside Italy and I had been thinking of setting the record straight by writing something about him. Now he has died I think that the time has come. to set out some of his achievements. Humi was born in Japan, but came to work as a nuclear scientist at the University of Padua in Italy. He later took Italian citizenship, perhaps to his regret because Japanese law does not recognised dual nationality and his Italian citizenship meant that he was unable to return to live permanently in Japan following his retirement and had to be content with short visits. Humi is bestknown for his formulation of the basic axioms of the geometry of paperfolding. As an adopted Italian, he followed a long tradition of Italian interest in the geometry of paperfolding, beginning with the Jesuit, Urbano d’Aviso (born in Rome in 169) and continuing with P. Pasquali in the 19th century and Giovanni Vacca, who wrote the first important review of paperfolding and its mathematics in an article published in the Italian journal, Periodico di Matematiche in January, 1930. Others had tackled the mathematics of paperfolding, one of the bestknown being T. Sundara Row of Madras in India. In the 1893 he wrote “Geometric Exercises in Paperfolding”, which is still in print. It was written for students in schools and while it included a method of trisecting an angle, something which set it apart form previous concepts of geometry, it was still firmly based in Euclidean geometry. The true mathematics of paperfolding still had to be written. I remember being very frustrated when I started my studies of paperfolding in the 1950s. My school geometry, based on Euclid did not seem to fit paperfolding, yet it was obviously firmly based in geometry. What kind of geometry was it? Quite apart from mathematics, being a Japanese living in Europe, Humi was uniquely placed to strengthen the links between paperfolders in Japan and the West. He spoke not only Japanese and Italian, but also spoke English well, so that he could communicate widely. The Italian origami society, Centro Diffusione Origami arranged to hold its convention for 1987 in Padua in 1987 and it was planned to incorporate a grand exhibition with the name of “La Luna Carta” in a large hall. Humi made the convention an opportunity for a special meeting between folders of Europe and Japan; folders from Japan and other countries were specially invited Italy was naturally represented by many folders including Luisa Canovi, Luigi Leonardi, Raffaele Leonardi, Giovanni Maltagliati and Roberto Morassi. From came France Genevieve de Gouvien SaintCyr and Jerome Cassalonga, from England, David Brill and Paul Jackson and from Japan, Yoshihide and Sumilko Momotani, and also Masiro Chatani, well known for popups of famous buildings. But perhaps the most significant guest of all was Tomoko Fuse, then scarcely known even in Japan. Humi had discovered in her a new approach to origami in her folding and he invited her to Padua. It was her attendance at this convention that brought her to the notice of the world’s paperfolders. Her presence at Padua started a in the origami community a worldwide loveaffair with her own kind of modular folding that has never abated. I once discussed Chatani’s popup architecture with Humi, Although Chatani’s work was not “origami” in its usual sense and, indeed, was more based on cutting than on folding, Humi vas very impressed by his art. Chatani was an architect and when he visited Italy he took the opportunity of viewing some of the notable buildings with a view to making “popups” of them. Chatani regarded his art as “Origamic Architecture”. His use of the word “origami” was controversial, although Humi did not comment on this. Two year later, Humi decided to build on the foundations of the Padua Convention by personally organising a conference to discuss Origami and Mathematics. Once again he planned it to be a meeting between Westerners and Japanese. The conference was given the name of “The First International Meeting of Origami Science and Technology” and was arranged to take place at the Casa di Lodovico Ariosto in Ferrara. This was the building where Professor Margherita Beloch, an earlier student of the geometry of paperfolding, had announced the discovery that using paperfolding it was possible to obtain roots of the fourth order, something which was impossible using Euclidean geometry, based on a straight edge and compasses. Belloch was Humi’s own main inspiration for his study of the geometry of paperfolding and he dedicated his proposed conference to him. The main difficulty was to prepare a list of invitees. Not everyone could be invited, and not everyone who was invited could attend. The conference was given the somewhat lengthy title of “The First International meeting of Origami Science and Technoogy”. When it opened on 6th December, 1989 a representative body of the world’s, mathematicians of Origami gathered together. Among those attending from Japan were Koryu Miura, Toshikazu Kawsaki and Yasushi Kajikawa. John S. Smith attended from England, Will Oosterbosch from Holland and Thoki Yenn from Denmark. Paulo Mulatinho, although not a mathematician came from Germany. Apart from Humi, himself, those attending from Italy included Emma Frigeri, Benedetto Scimemi, Pier Luigi Lucio, Luigi Pepe and Roberto Morassi. A special address was given by Maria Papparo. This was not about mathematics, but was about her successful use of origami in drug therapy. Her account of how origami was used to cure a drug addict inspired John Smith to organise the first Conference of Origami in Education and Therapy two years later (COET 91). Lectures were very varied from the relatively pure origami of Roberto Morassi’s “The Elusive Pentagon” to Thoki Yenn’s inimitable excursion through mathematical curiosities to the higher mathematics of Emma Frigerio and Toshikazu Kawasaki. Perhaps, however, the most significant contributions were those of Humi himself and in particular his paper on “An Axiomatic Development of the Origami Geometry” which worked out the basic axioms of the subject and which have laid the foundations for future research. The main force of the Meeting was the mathematics of Origami and not, as its name would imply the experimental science of Origami or its application in technology. Nevertheless, Professor Miura’s now famous map fold, was an example of origami applied to technology and Wil Oosterbosch briefly spoke about the folding of a Miura map by machine. Not content with organising the conference, Humi went on to edit the Proceedings, which he published himself. The Proceedings not only reproduce the papers which were read at the meeting, but they also reprint many other significant papers on the subject of mathematics and paperfolding. The Proceedings begin by reproducing several of the papers written by Professor M. Piazzola Beloch. They also include papers by Michel Mende’s France and Jacques Justin as well as earlier papers by Humi and by Toshikazu Kawasaski. Because of the incorporation of these older papers, the Proceedings of the First International Meeting of Origami Science and Technology are an invaluable springboard for the study of the mathematics of Origami. In view of the growing interest in the mathematics, science and technology of Origami it is unfortunate that they have been outofprint for several years. The Ferrara Meeting was the inspiration for a second conference devoted to Origami and mathematics, which was held at Otsu, near Kyoto in Japan in November and December, 1994. While he may have been consulted, and was certainly the inspiration for the conference, Humi was not directly concerned with its organisation. The conference was named “The Second Meeting of Origami Science and Scientific Origami”. However, it expanded to include origami design, origami in education and the history of paperfolding. The organisers included Koryu Miura, Tomoko Fuse, Toshikazu Kawasaki and Jun Maekawa. It was immaculately organised and many folders of all approaches came from around the world to what was probably the greatest origami convention of all time. It was a rich gathering of many of the world’s finest folders and origami theorists. Even Akira Yoshizawa, who was wellknown for his opposition to “geometrical” origami attended and spoke, strongly advocating his own artistic approach to Origami.. Humi attended as a private person and read a paper written jointly by him and Shuzo Fujimoto. He also read a paper by himself on “Right Angle Billiard Games”. Humi was not prepared for any honours, but during the opening session he was called up to the platform to sit among the organisers and officials. It was a tribute that he fully deserved because if it had not been for Humi’s meeting in Ferrara, the second meeting at Otsu would not have taken place. Since then the Ferrara meeting and its successor at Otsu have inspired a meeting about mathematical origami at in California in Astilomar in California. In March, 2003 and further meetings about origami mathematics and science are planned. As a result, the mathematics of Origami is now the subject of vigorous discussion in the academic world, with many brilliant mathematicians increasingly engaged. Scarcely a day passes by without the announcement of some discovery in origami mathematics, science and technology. Humi may have been a scientist and a mathematician, but he was a also a warm human being. A vivid memory of Humi arose out of an incident which followed a convention of Origami Deutschland held at Freising, near Munich in the early 1990s. Some children from Chernobyl had been invited to Munich from Russia to give them a break form the stillpolluted air of the Chernobyl region. The paperfolders who attended the Convention were invited to teach the children origami at a school just outside Munich. We duly travelled to the outskirts of Munich and taught our origami, to a group of very charming children. Outside some toys for the children had been provided and some of the children were playing in the sunshine. My lasting memory of Humi, nuclear scientist though he was, is of him spending most of the time in sheer delight riding a small child’s bicycle round the playground! Humi’s memorial will be his contributions to the convention at Padua in 1987, his organisation of the Meeting at Ferrara in 1989 and his production of the Proceedings of that Meeting. He will be remembered for his singlehanded editing and publishing of the Proceedings of the Ferrara meeting. But above all, he will be remembered for just being Humi. David Lister. Revised 2nd April, 2005. 

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