what's the application?

pi can be the base if you want it to be.

https://en.wikipedia.org/wiki/Non-integer_representation

e.g a circle with a radius of 1π will have an area of 10π, you don't have to count in base 10.

The question is about an number system that has a different natural number base - a number from the sequence
1,2,3,4,5,6,7,8,9,10,11,...etc

The thing is that pi 3.1415..... isn't necessarily a very long DIGITAL sequence for the remainder in another base a non-digital (non-10) base

I may not get the context of your question and I am not sure if I can be of any assistance but let me come up with it anyway.

Complex numbers use a different base, but I do not recall how they work. Sure you'll find stuff on wikipedia. Anyway PI is a math constant and will therefore always stay the same even if you use the arc math. That is the good thing about a constant. If it is about the length of the number, why don't you cut it short? Your calculations will be approximations anyways. Won't they?

Let me know how things work out :-)
Cheers

Thanks for the reply.

Perhaps on another note how to they compute Pi?
Is it an iterative formula?

I remember using PI in those calculations but PI can only be calculated by going back to its roots. There are different ways, i.e. Archimedes developed a formula using a polygon with infinite corners to approximate a circle. There are other ways but they all end up describing the same thing and in terms of numbers the result always starts with 3.14. So PI can not be iterated as it is an infinite geometrical description. That is why the numbers after the comma are endless and do not repeat a pattern. And it has been calculated several times, so do not quite understand why you would want to do that. May I ask you what you are going to use it for?

So if I were to programm an algorithm or something (assuming PI is not set as a constant by default) I would define a variable and give it the value of 3.14. That is it. Otherwise I will need all the CPU just to calculate that number and I do not assume that is you goal.

cheers

Thanks for the reply.

I'll look for the formula that they use.

I am not looking for a decimal value for PI. Clearly that is known to many more DECIMAL places than I would need. (the spreadsheet @PI function gives 3.14159265358979).

----------------
Comparing 10 and 12:

IF you have a 12 base then
if I ask for 1/2 you say 6
if I ask for 1/3 you say 4
if I ask for 1/4 you say 3
if I ask for 1/6 you say 2

IF you have a 10 base then
if I ask for 1/2 you say 5
if I ask for 1/3 you say 3.333333333333333333333333333333333333333333333333333333
if I ask for 1/4 you say 2.5
if I ask for 1/6 you say 1.111111111111111111111111111111111111111111111111111111

The number base chosen changes the complexity of the remainder (in the above example).

The original question, i.e. would a different number base (different from base ten) give a simpler remainder?

So in asking the question I thought a math whiz might say:
"not sure let me think on it"
and then
"Interesting using base ... x ... the value is x.fg






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c. 250 BCE Archimedes[1] 223 / 71 < π < 22 / 7