InCEPTIO: Vesica Piscis as a Receptacle for Metallic Ratios

Abstract

This research penetrates the grounded theory of Vesica Piscis and provides novel insights on the traditional view of Vesica Piscis to be a powerful and key symbol that masters in creating a complexbut simple portrayal of the members of Metallic Mean Family in unification. Circles have emerged tohave idiosyncratic features as they have the formidable potential to create patterns as well as sculptthe theoretical understanding and applied methodologies by humans. Amidst such knowledge attributedto circular forms, the most primordial one is the Vesica Piscis symbol. Numerous analyses of VesicaPiscis and its commonality in constructions have been conducted and especially this symbol found acommon ground for deriving the Golden Ratio

however, the successive members of the Metallic MeanFamily (MMF) after the Golden Ratio such as Silver, Bronze, and Copper Ratio, etc. have not been fullyelucidated. Also, no fundamental recursive geometry or pattern has been proposed to derive all of theratios of the Metallic Mean Family in succession or in an unbroken sequence. This raises a question: canVesica Piscis possibly generate other Ratios of the Metallic Mean Family as well? The act of drawingVesica Piscis (comprising two circles of the same radius) in recursive pattern and creating the famedGolden Ratio as a baseline can feasibly generalize the entire family of Metallic Ratios and will expand themathematical and computational perspective related to this symbol and inter-relate its applicability indesign. The symbol Vesica Piscis offers a formidable potential to create a geometric progression patternthat results in the entire MMF in a geometric sequence. An irrational number 1.618 (Phi), also known asthe Golden Ratio, is a geometrical concept that mankind has known since the time of prehistoric Greeks.In this research, we foremost propose to understand how the twin circles of Vesica Piscis can affect thegeometry of the Golden Ratio and successive members of the Metallic Mean Family (Silver, Bronze, andso on). Vesica Piscis has emerged in the illustrations of several religions including Christianity. Thisstudy will not only provide the mathematical and geometric generalization for Metallic Mean Family butalso uplift the view of this symbol from a religious context towards more computational mathematicsand design applications. This work deeply examines the space within the Vesica Piscis as a potentialcontainer or bearer of ‘‘The family of irrational numbers’’, i.e., Metallic Mean Family comprising Golden,Silver Ratios, etc. Furthermore, we also aim to highlight the fact that this simple shape can advanceinto sequential and robust patterns composed of the members of the Metallic Mean Family.