Help in calculating the square of a number in sexagesimal notation?

[moohah]

How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it would be appreciated! Thanks in advance for answers...

 

[gopher_p]

Some questions to think about that might lead to an answer to your question ...

How do you go about calculating a number's square in decimal notation?

Why/how does that work?

Why does that not work for a different base? Could you change something to make the process work in a different base?

 

[lurflurf]

(a +b x+c x^2)^2=a^2+2abx+2acx^2+b^2x^2+2bcx^3+c^2x^4
let
a=37
b=4
c=55
x=1/60
then carry

 

[Integral]

First step would be to define symbols for your 60 integers, then work out multiplication and addition tables in terms of those integers, now multiply.

The trouble with lurflurf's solution is that it is doing the arithmetic in decimal, and the result will be in decimal.

 

[jackmell]

As long as lurflurf does his arithmetic in base-60 arithmetic, I believe his method would correctly compute the base-60 square of that number in base-60 notation.

Personally I think the OP should first do some simple ones. How about octal? Won't that work with the number he gave or even a simpler number? Try squaring some simple numbers in just plain-old octal first, then ramp it up.

 

[lurflurf]

^No that is sexagesimal. We could use a=10 z=35 A=36 X=59 to conform with convention

B.4T=B*1+4*0.1+T*0.01

for one example
a.bc
is perfectly adequate

 

[jackmell]

. . . I don't know what none of you guys are doing in this thread to be honest with you. It's ambiguous, unclear, and confusing to someone at the top in class.

 

[moohah]

Hey lurflurf has it right... thank you guys for your help