New Number Class: Diagonal Numbers II

A preface briefly lays out object of essay, to correct my previous essay of the same name. Chapter 1 takes an abstract from New Number Class: Diagonal Numbers with my correction note. Chapter 2 demonstrates a theorem that only number bases with an integer root can produce perfect roots of numbers such as 2, 3, etc. Perfect Root has the sense that the rightmost digit of the mantissa of the square roots can be zeroed out. We show that bases such as base 10, 12, cannot do this. Their roots are irrational. We discuss problems of diagonals, arcs and their relationship to orthogonal numberlines and Cartesian grids. I still remain perplexed about diagonal lines, and sense that more needs to be done on this matter. I briefly discuss a past concept of computing with mixed number bases on computers to deal with rounding problems, and wonder if this would be worthwhile.