A Proposal for a Japanese Keyboard on Cellular Phones

Margenstern, Maurice; Martin, Benoît; Umeo, Hiroshi; Yamano, Shogo; Nishioka, Kazuhiro

doi:10.1007/978-3-540-79992-4_38

Cited by 7 publications

(4 citation statements)

References 3 publications

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“…Before turning to this study, let us mention a few applications of the pentagrid and the heptagrid. Among those quoted in [9], let us mention the colour chooser using the heptagrid, see [1], the Japanese keyboard for cellphones using the pentagrid, see [12] and the communication protocol between tiles of the pentagrid or the heptagrid, see [7,11].…”

Section: Extension Of the Splitting To Other Tilingsmentioning

confidence: 99%

An application of Grossone to the study of a family of tilings of the hyperbolic plane

Margenstern

2012

Applied Mathematics and Computation

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In this paper, we look at the improvement of our knowledge on a family of tilings of the hyperbolic plane which is brought in by the use of Sergeyev's numeral system based on grossone, see [17,18,19]. It appears that the information we can get by using this new numeral system depends on the way we look at the tilings. The ways are significantly different but they confirm some results which were obtained in the traditional but constructive frame and allow us to obtain an additional precision with respect to this information.presented in this paper are slightly different from those briefly presented at the International Workshop Infinite and Infinitesimal in Mathematics, Computing and Natural Sciences held at Cetraro, Italy, in May 2010, see [13]. They are in some sense a more precise version of what was given in [13]. In Section 6 we indicate a few possible continuations. The new numeral systemIn papers [17,18,19], Yaroslav Sergeyev gives the main arguments in favour of the new numeral system he founded, allowing to obtain more precise results on infinite sets that what was obtained previously.We can sum up the properties of the system as follows.We distinguish the objects of our study from the tools we use to observe them. These three parts of the knowledge process have to be more clearly distinguished as they were traditionally in mathematics, contrarily to other domains of science, as physics and natural sciences where this distinction is clearly observed. This is the content of Postulate 2 in the quoted papers. It is an important issue for mathematics where the distinction between an observer and what is observed is very often forgotten. In particular, not enough attention is paid to subjectivity of the observer and the relative validity of his/her observations. The latter are very dependent of cultural elements, especially the language used by the observer to describe what he/she sees.We are interested in the properties of the objects, some of them being possibly infinite or infinitesimal, but operations on the objects, performed by a human being or a machine, necessarily deal with finitely many of them and only finitely many operations can be applied within the frame of an argument. This is the content of Postulate 1 in the quoted papers.At last and not the least, we consider that the principle The part is less than the whole has to be applied to all numbers, finite, infinite or infinitesimal, and also to all sets and processes, whether finite or infinite. This is the content of Postulate 3 of [17,18,19].On the basis of these principles, Yaroslav Sergeyev introduced a new numeral system in order to be able to write down infinite numbers. To this aim, an infinite natural number is introduced, grossone, denote by 1 , which is the number of elements of the set of positive integers. This number satisfies the following three properties which are axioms of the system: − for any finite natural number n, n < 1 .− we have 0. 1 = 1 .0 = 0, 1 − 1 = 0, 1 1 = 1, 1 0 = 1, 1 1 = 1 and 0 1 = 0. − let IN k,n be the set of p...

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Section: Extension Of the Splitting To Other Tilingsmentioning

confidence: 99%

An application of Grossone to the study of a family of tilings of the hyperbolic plane

Margenstern

2012

Applied Mathematics and Computation

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“…The use of the pentagrid and the fact that hiraganas and katakanas of the Japanese language are traditionally presented in series based on the five vowels of the language inspired me the idea to use the same grid but this time, in a Japanese environment. We did some work in this direction, with Japanese colleagues, see [8]. Figure 10 illustrates the principle of the working.…”

Section: Japanese Keyboardmentioning

confidence: 99%

Navigation in tilings of the hyperbolic plane and possible applications

Margenstern

2009

Preprint

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“…In a previous paper, [4], the first author presented a proposal for a Japanese keyboard for cellphones. He presented his ideas first at AUTOMATA'2005 in Gdansk, Poland.…”

Section: Introductionmentioning

confidence: 99%

“…They highly appreciated the project and decided to join it. Later on, we call the project described in [4] as the Japanese project.…”

Section: Introductionmentioning

confidence: 99%

A proposal for a Chinese keyboard for cellphones, smartphones, ipads and tablets

Margenstern,

2013

Preprint

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A Proposal for a Japanese Keyboard on Cellular Phones

Cited by 7 publications

References 3 publications

An application of Grossone to the study of a family of tilings of the hyperbolic plane

An application of Grossone to the study of a family of tilings of the hyperbolic plane

Navigation in tilings of the hyperbolic plane and possible applications

A proposal for a Chinese keyboard for cellphones, smartphones, ipads and tablets

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