A STUDY ON THE CYCLIC NUMBER PATTERN ON THE TORUS

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  • 円環面上のサイクリックナンバーパターンについて
  • エンカンメンジョウ ノ サイクリック ナンバー パターン ニ ツイテ

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Abstract

This study is one attempt of developing a system of preferred modular sizes in building. For the practical means to control the decentralized development of the previous series like a development of the EPA numbers or doubling series, this system choices the sexagenary one and deals with numbers arranged in theoretical orders in a limited system mingling with the decimal system. The reason to choice the number 60 of the sexagenary are : 1. The boundary number is to be larger than number 40 of the Renard Series R 40 which is used in engineering science, for the complexity of the building industry, but to be not so large as 90. 2. The number should have more divisors as much as possible for the flexibility. This sexagenary system allows to get the secondary or tertiary numbers, for example 84 or 180 like a calling of clock's number, for example 14 o'clock or 20 o'clock, and allows also in this case for multiplication of all sizes by 10 like the present Japanese System to an increased series of modular sizes. For the Systematic presentation of 60 numbers limimed in sexagenary, the arrangement is developed on the torus, of which the character is to have many rings and spiral rings on the surface which may allow the continuity of the numerical circulativity like the clock system. (Fig. 27, 29, 31) The principal series on the torus have respectively the increment of 2, 3 or 5, which are three primary themes for the practical purpose and have also the Fibonacci's character. And then the series having increment of 6 can be found easily. This numerical arrangement of the sexagenary system on the torus has many mutual numerical relations among adjacent numbers (Fig. 11, 12) and has many arithmetical series which are more useful than progressive for the system of preference for numbers for use as the numerical factor in multimodular sizes for vertical and horizontal dimensions in building. This study may expect to make a start point for revising JIS A 0001 Architectural Module in Japan for the practical purpose.

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