Website Map for the “Transdecimal Observatory“

This site map covers content present at regarding elementary number theory. The working title of this segment of the Vinci LLC website is the “Transdecimal Observatory”, dedicated to the study of the mechanics of number bases, especially those larger than decimal. The superior highly composite numbers, primorials, and the range of integers 2 < r <= 120 are of greatest interest. The relationship between digits of r, any n such that 0 < n <= r (where 0 is used to signify congruence with r) is of great interest. Composition of r and n, their relationship, and the number-theoretical aspects of n as it relates to practical applications of some base r are the subject of study. The “lingua franca” number base used in the Observatory is pure sexagesimal, as it is a five-smooth superior highly composite number. Pure sexagesimal is expressed using Michael De Vlieger’s “argam” numerals. Other commonly used bases are 12, 120, 360, and 2520, the last of these expressed as a mixed radix, base 42 on base 60. Currently the Transdecimal Observatory contains PDF versions of work and is limited to this format. The Observatory is a work in progress. Visit again soon!

Vinci LLC
Home Page → (Digital visualization of construction and the built environment)

Argam Numerals
Argam numerals in the argam font.
Argam Hexadecimal and Sexagesimal Numerals
Argam Sexagesimal Numerals
Argam Kinoctove numerals to represent bases up to decimal 360. Some earlier versions include argam-ajamyse and argam-arimaxa.
Argam Calendar (2010) in duodecimal and sexagesimal argam. Four-digit duodecimal dates at right are the basis of Vinci LLC project numbers.

Base 60 / Sexagesimal
Argam Sexagesimal Numerals
Direct multiplication table showing all 1830 unique values
Direct multiplication table (2009 version)
Factor Study showing multiples of pairs of distinct prime divisors
The Reciprocal Divisor Method for sexagesimal multiplication (7 Mb)
Abbreviated multiplication table for use with the RDM

Number Bases in General
Balance Study, examining divisors and totatives across number bases
Cyclic Resonances, a study of the geometry of number bases
Digit-Base Relationships, a study of the digits of number bases to 120
Digit-Base Presentation, a recent presentation on digits and number bases (loads in Safari).

Duodecimal Work
Much of this work resides at the Dozenal Society of America’s website,, which he manages since 2008.
Michael De Vlieger has remastered many of the DSA’s downloadable documents.
Multiplication tables in various bases.
Analysis of multiplication tables, applying the “digit-base relationship” concepts.
Synopsis of duodecimal numeral systems.
Michael De Vlieger is a past Editor of the Duodecimal Bulletin, see issues published between 2008-2014 at the DSA archive.

This page last modified Saturday 9 January 2016.