The Number Base
Established 2013

5106 Hampton Avenue
Suite 205
St. Louis, MO 63109-3115

Phone 314-351-7456

mike@numberbases.com

The Number Base

Mission statement

This website aims to explore integer number bases in terms of their elementary relationships with their digits, assessing these as facilitators of human arithmetic. The analyses employ digit maps, which serve as simple visual tools that synopsize these relationships.

“The Number Base” is a project initiated in summer 1991 in a notebook, and again in 2007 by Michael Thomas De Vlieger, designer and developer of the digit map concept. The work presented on this site is largely original but draws on elementary number theory. This page is an enabling installation intended to set up web analytics ahead of the live date so that visits can be measured. It was intended to be live 22 October 2012. The live date is 28 January 2013.

Sample of work appears below. See an example of a digit map, and a glossary that defines some of the concepts used to generate the map. See the proof of concept in the form of a menu to various pages of content at this forum post. (This page is experimental as of 17 October 2012).

The Digit Map.

      Digit Maps for Bases 2 ≤ r ≤ 30
2 0 1    
3 0 1 2    
4 0 1 2 3    
5 0 1 2 3 4    
6 0 1 2 3 4 5    
7 0 1 2 3 4 5 6    
8 0 1 2 3 4 5 6 7    
9 0 1 2 3 4 5 6 7 8    
10 0 1 2 3 4 5 6 7 8 9    
11 0 1 2 3 4 5 6 7 8 9 10    
12 0 1 2 3 4 5 6 7 8 9 10 11    
13 0 1 2 3 4 5 6 7 8 9 10 11 12    
14 0 1 2 3 4 5 6 7 8 9 10 11 12 13    
15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14    
16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15    
17 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16    
18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17    
19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18    
20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19    
21 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20    
22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21    
23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22    
24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23    
25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24    
26 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25    
27 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26    
28 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27    
29 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28    
30 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  
  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Legend

Unit, 1 | r ∧ 1 ⊥ r

Divisor, d | r

Semidivisor, g = ∏ piδ ∧ (δ > ρ) ∧ (g ¬| r) ∧ (0 < g ≤ r)

Semitotative, h = ∏ piqj ∧ (0 < h < r)

Totative (opaque), t ⊥ r ∧ 0 < t < r

α-Totative, tα ⊥ r ∧ , tα | (r + 1)

ω-Totative, tω ⊥ r ∧ , tω | (r − 1)

α/ω-Totative, tα ∧ tω

 

This page last modified Monday 22 October 2012.