A Figure Analysis of the Three-pole Amida-kuji with Non-consecutive, Alternating Bridge Patterns: A Summary of the Relationships within its Variables in Mathematical Models

Abstract

Amida-kuji is a Japanese lottery game perceived as a matter of chance or probability. It consists of vertical lines that serve as the poles, and horizontal lines as the bridges. This game can be simply explained as a token entering a maze that ends to one specific outlet. The token always moves down unless it will encounter a horizontal line or bridge. As books, journals and researches are reviewed, there is no available material that describes thoroughly the scientific concepts involved within the system. Hence, this study is made with the humble attempt of undermining principles and theories that can be explained and defined by mathematical philosophies and properties. Specific figure conditions were made according to the number of its bridges. Each figure was labelled using the ratio of addends of the bridge, representing the number of bridges per pair-pole. Bridges were placed alternating from one pole-pair to the other. This means that no two consecutive bridges can connect the same pair of poles. After classifying figures with similarities and patterns, formulas were derived based on constants and relationships observed. It shows that there are some sequential patterns in the number of bridges and path-turns in an Amida-kuji figure with alternating bridges. Thus, the formula for the arithmetic sequence was applied. There are three classifications formed namely Green, Blue, and Yellow-type figures and each has derived formulas to get the number of path-turns (〖PT〗_n), nth term of the bridge (b_n), and Difference in Arithmetic Sequence (d_ASn). Green-type Amida-kuji figure has a uniform a number of path-turns, Blue-type Amida-kuji figure has 2 similar numbers of path-turns that are 2 less than the other and Yellow-type Amida-kuji figure has 2 similar numbers of path-turns that are two greater than the other. The derived formula will have a great contribution to engineering and architecture. One probable area in this study can tap is mapping and route management concepts. It’s noticeable that a map is a diagrammatic representation of the physical features of an area which can perform to the linear features of Amida-kuji. Overall, patterns and sequences can be an essential foundation for building new ideas and innovations.