1.6.2  
Circle Numbers  
home page  
Circle numbers represent magnitude using a depthvalue notation that supports a maximally factored form, as opposed to conventional HinduArabic numbers that use placevalue to represent magnitude in a polynomial form. Both use a uniform base; both support an arbitrary choice of base value. The factored circle form provides distinct computational advantages, at a slight cost to ease of readability. Maximally factored numbers are clumsy when expressed in conventional notation, but quite elegant when expressed in a boundary notation. More fundamentally, boundary notation shows that the foundational properties of group theory are largely syntactic. 

boundary math  
numerics  


number systems  
∆ circle numbers  
graph numbers  


links  
site structure  
Conventional polynomial and factored boundary forms of binary twelve: Three animations follow. They each display the same materials, but with varying degrees of condensation. CIRCLE NUMBERS ANIMATION (complete version, 11 minutes) CIRCLE NUMBERS ANIMATION (condensed version, 4 minutes) ADDITION AND MULTIPLICATION OF CIRCLE NUMBERS (short version, 2:20 minutes) 
