Register to reply 
If a irrational number be the basis of count 
Share this thread: 
#1
May214, 01:18 PM

P: 686

In the comum sense, the number 10 is the base of the decimal system and is the more intuitive basis for make counts (certainly because the human being have 10 fingers). But, in the math, the number 10 is an horrible basis when compared with the constant e. You already thought if an irrational number can be the basis of system of count, it make sense?



#2
May214, 01:43 PM

Mentor
P: 18,019



#3
May214, 03:14 PM

Sci Advisor
P: 6,027

For arithmetic to work easily, the basis has to be an integer. It is hard to envision what a number would even look like with e or any noninteger. Since computers became widespread, 8 or 16 might be practical alternatives to 10. 


#4
May214, 06:49 PM

Sci Advisor
PF Gold
P: 3,498

If a irrational number be the basis of count
Have any of you folks ever converted everyday numbers to noninteger radixes?
I tried back in the late seventies, just out of curiosity but my math was not up to the challenge. I wanted to see what would some of the physical constants, planck, c, μ_{0} , ε_{0}, look like in bases e pi etc. Closest i ever came was a Basic program that converted Florida's lotto numbers into 49 bit binary numbers and printed them out as hex, decimal and octal. No visual patterns emerged. Your links above are quite interesting. old jim , who is distractable to a fault. 


#5
May214, 07:20 PM

Mentor
P: 21,216




#6
May214, 08:44 PM

Sci Advisor
Thanks
P: 3,418

Many years ago, when one of my daughters was in grade school... Over dinner she asked me what was the most "interesting" base for a number system.
I answered ##2##, because ##1+1=110## and you can get the rest of arithmetic from there. What I didn't know was that the question was prompted by a school homework assignment: Choose a radix and demonstrate worked addition, subtraction, multiplication, and long division problems in that radix. She pulled it off, although the long division algorithm is not deterministic  when dividing ##A## by ##B##, having ##nB\le{A}## and ##(n+1)B\gt{A}## doesn't mean that subtracting ##nB## is the right next step. 


#8
May214, 10:03 PM

Sci Advisor
Thanks
P: 3,418




#9
May314, 02:15 AM

Sci Advisor
HW Helper
PF Gold
P: 3,164

I remember learning about different bases when I was in grade school, maybe 4th or 5th grade. This was in the late '70s, around the tail end of the "new math" era. For some reason base 7 was often used in examples, if I recall correctly. We also learned about the commie metric system before Reagan abolished it.



#10
May314, 07:20 AM

P: 686




Register to reply 
Related Discussions  
Square Root of an Irrational Number is Irrational  Calculus & Beyond Homework  26  
Irrational number to an irrational power  Precalculus Mathematics Homework  13  
Irrational power of an irrational number  Precalculus Mathematics Homework  5  
Irrational number approximation by a rational number  Linear & Abstract Algebra  6  
Count the number of integer solutions  Calculus  1 