I am often amazed by how accurate a decimal numeral system is to describe the mathematics world. A lot of things feel very logical like the result of any multiplication by 5 will always end with a 0 or a 5. Or this again with this rule: a number is divisible by 3 if the sum of its digits is divisible by 3.(*)
Bu I wonder if a binary or an octal or a hexadecimal wouldn't have more of these rules, that would make the understanding of maths even simpler. I guess we have the decimal numeral system in Occident because we have 10 fingers, but this doesn't mean it's the more efficient way of understanding all the maths logic. We use the Qwerty keyboard but it's not the most efficient keyboard around.
So in brief my questions are:
- Is the decimal numeral system the most efficient one to understand the mathematics rules and patterns of the universe, geometrics or simple multiplications/divisions?
- Is not, which one is the best?
*) I am only using this two rules as examples because I don't know a lot of others maths patterns like those one. But I would be interested in knowing if others patterns, (I am tempted to say, more important patterns), exists in other number systems, that don't exist in the decimal one.
Best Answer
Similar properties apply to a multiple of d in base b, if d divides b.
Similar properties apply to a multiple of d in base b, if d divides $b-1$.