The study details specified properties of whole numbers in conjunction with repetitive arrays and sequences. There prevails a common pattern for numbers when they exist in defined structures. The paper extends to the scope of progressions in regard to the specific number relationships and its reach in advanced mathematical studies. The properties of numbers enumerated have its scope in the field of recreational mathematical theories as well. Finding 01 proves the relationships between numbers in specific patterns, with exceptions in effect. The exceptions hold true only in the mentioned patterns of numbers. Findings 02 and 03 show the properties of numbers in Arithmetic Progression and the relationship of the numbers in specific arrangements with the Common Difference. Findings 04 and 05 work on the value of Determinants of matrices of which numbers are in Arithmetic and Geometric Progressions and its application in regard to positioning of multiple points in varying dimensions. Findings 06, 07 and 08 detail the unique properties of numbers when applied in addition, subtraction and multiplication and the ‘CONSTANCY’ in the end results. Findings 09 and 10 explain the relationships and properties of numbers with reference to the structures of regular polygons and the positioning of points in multiple dimensions.
Keywords: relationships multi – dimensional locales, specified arrays, whole numbers
