03/01/2016, 10:15 PM
The name spiral number comes from the analogue of polar coördinates.
Multiplication is identical just without the mod 2 pi for the angle r.
Visually this means that multiplication is on a spiral rather than on a plain or circle ( as with the complex Numbers ).
Hence " spiral numbers ".
To have a meaningful connection between addition and multiplication , I required the distributive law.
Overview of typical distributive Numbers with invertible operators and a unit (?)
1) commutative and associative
Rings , grouprings.
Iso to copies of R and C ( when algebraicly closed ).
2) noncommutative and associative
Matrices.
3) commutative and nonassociative
Tommy's spiral Numbers
4) noncommutative and nonassociative
No intresting cases known unless anticommutative (Lie).
???
Not sure how this gets us " fractional dimension " or " new Numbers for tetration ".
Feel Free to correct or improve.
Regards
Tommy1729
Multiplication is identical just without the mod 2 pi for the angle r.
Visually this means that multiplication is on a spiral rather than on a plain or circle ( as with the complex Numbers ).
Hence " spiral numbers ".
To have a meaningful connection between addition and multiplication , I required the distributive law.
Overview of typical distributive Numbers with invertible operators and a unit (?)
1) commutative and associative
Rings , grouprings.
Iso to copies of R and C ( when algebraicly closed ).
2) noncommutative and associative
Matrices.
3) commutative and nonassociative
Tommy's spiral Numbers
4) noncommutative and nonassociative
No intresting cases known unless anticommutative (Lie).
???
Not sure how this gets us " fractional dimension " or " new Numbers for tetration ".
Feel Free to correct or improve.
Regards
Tommy1729
