# Christmas brain twister.

#### Bogart

##### Active Member
Is there a base number system where pi is a rational number?

I don't know the answer to this, I was just wondering.

#### Urakro

##### ~
Where the base number itself is pi. It would be the first rational number after 0.

#### Seteleechete

##### Together forever
Decided to google it
" I think people are missing the point of the question. It's not "can you write pi in such a way that it terminates," it's "can pi be a rational number." Those are two different things.
Irrationality is not defined as "the number doesn't terminate." That's a property that irrational numbers have when you write numbers in an integer base, but it's not what makes a number irrational. There are plenty (an infinite number) of rational numbers that don't terminate. An irrational number is a number that cannot be expressed as a ratio of two integers (whole numbers).
Writing pi in base pi makes it "look like" a rational number, but it doesn't have the same properties as one. It's still not a ratio of two integers: the set of integers does not change when you use a different number base."

wow I know I am really bored when I actually google something...

#### Bogart

##### Active Member
Where the base number itself is pi. It would be the first rational number after 0.
This was an expected answer and the answer you might find from a standard google search. However, as I tried to define pi as 1, I realized it would still be a symbol for an unquantifiable value, causing all numbers to be irrational. That's what I would call Dr Seuss math. Which is when I figured out how to answer the OP's question.

In base pi how would you express this roman numeral: XIV?

#### Bogart

##### Active Member
Decided to google it
" I think people are missing the point of the question. It's not "can you write pi in such a way that it terminates," it's "can pi be a rational number." Those are two different things.
Irrationality is not defined as "the number doesn't terminate." That's a property that irrational numbers have when you write numbers in an integer base, but it's not what makes a number irrational. There are plenty (an infinite number) of rational numbers that don't terminate. An irrational number is a number that cannot be expressed as a ratio of two integers (whole numbers).
Writing pi in base pi makes it "look like" a rational number, but it doesn't have the same properties as one. It's still not a ratio of two integers: the set of integers does not change when you use a different number base."

wow I know I am really bored when I actually google something...
I didn't realize this was an ambiguous question when I asked it. Thank you for clarifying. I don't mind if everyone googles it, but I doubt you will find the answer in one place. I just wiki'ed the value of pi and they have it nailed down to 26 trillion digits or so and still counting (this is below Planck value I think). I find the question important because we are trying to define a naturally occurring phenomenon using our manifestation of value. Pi's value is quantifiable if you know the principle (R*2)pi but you cant nail it down with the language in our math.

Edit: I just went back and read your reddit link, I originally thought those were your words. There were educated people commenting on there and there were people who were uneducated commenting on there. Most of the people commenting weren't addressing the root of the question and left holes in their explaination.

#### Blarraun

##### straightedgy
In base pi how would you express this roman numeral: XIV?
What does a roman notation have to do with your question?

Roman XIV is 14, isn't it easier to write 14 in your question?

Is it to make yourself more difficult to understand?
Is there a base number system where pi is a rational number?
Writing pi in base pi makes it "look like" a rational number, but it doesn't have the same properties as one. It's still not a ratio of two integers: the set of integers does not change when you use a different number base."

#### Bogart

##### Active Member
What does a roman notation have to do with your question?

Roman XIV is 14, isn't it easier to write 14 in your question?

Is it to make yourself more difficult to understand?
I actually thought that would be clearer than trying to define an arbitrary quantity by using the numerical code we are talking about. In base pi there would be no 1 or 4, so to ask what the expression 14 is clouds my ability to distiguish base ten value from the newly defined base pi value. The difference between roman numerals and base pi is much more quantifiable. Even tho roman numerals are still based on base 10 calculation.

The question me and you might want to explore with eachother is: why did my attept to reduce general entropy resulted in localized increase in entropy between you and i?

#### Bogart

##### Active Member
You must have been editing while i was responding.

I tend to agree that the answer is no. But if thats the case, we have the structure of the universe and a very good desription of what it looks like and how it functions. The thing is that it fits my model.

#### Blarraun

##### straightedgy
I actually thought that would be clearer than trying to define an arbitrary quantity by using the numerical code we are talking about. In base pi there would be no 1 or 4, so to ask what the expression 14 is clouds my ability to distiguish base ten value from the newly defined base pi value. The difference between roman numerals and base pi is much more quantifiable. Even tho roman numerals are still based on base 10 calculation.
Do you know what is redundancy and why it's useful to get your message across?

There's a general way of expressing and naming the common base numeral systems which you are familiar with asking questions about such systems.

You can call your 14 a:
14 (10) or 14 (dec) or 14 decimal

And you avoid wasting time and confusing anyone who participates.
I tend to agree that the answer is no. But if thats the case, we have the structure of the universe and a very good desription of what it looks like and how it functions. The thing is that it fits my model.
And so?
So far the only non-redundant extension to what has been said is your observation that:
Pi's value is quantifiable but you cant nail it down with the language in our math.

#### Bogart

##### Active Member
Do you know what is redundancy and why it's useful to get your message across?

There's a general way of expressing and naming the common base numeral systems which you are familiar with asking questions about such systems.

You can call your 14 a:
14 (10) or 14 (dec) or 14 decimal

And you avoid wasting time and confusing anyone who participates.

And so?
So far the only non-redundant extension to what has been said is your observation that:
Im sorry, i didnt make it that far in school, but it appears to me that you still havent grasp the question: In base pi how would you express this roman numeral: XIV? The question its self is to help the ponderer come to the conclusion that the symbols we use in base 10 calculation are too coherent to use in base pi, roman numerals are even less coherent than the integer system we use. I think the redundancies you are refering to are designed to explore the realative value of the quantities we place on these symbols.

#### Blarraun

##### straightedgy
Im sorry, i didnt make it that far in school, but it appears to me that you still havent grasp the question: In base pi how would you express this roman numeral: XIV? The question its self is to help the ponderer come to the conclusion that the symbols we use in base 10 calculation are too coherent to use in base pi, roman numerals are even less coherent than the integer system we use. I think the redundancies you are refering to are designed to explore the realative value of the quantities we place on these symbols.
You didn't make it this far in school to learn about decimal system but you did advance enough to know about numeral systems in general which led you to asking about pi base system.
I'm tempted to look up your curriculum to confirm that decimal system is explained in the first grade of mathematics in elementary school, but I know you aren't serious.

Decimal system is the first example of a numeral system, there's no way you haven't heard of it if you've heard of base pi and you fully understand what a numeral system or base pi mean.

So your argument is that arabic numerals are too coherent and therefore roman numerals should be used to allude to your point that decimal system is incompatible with the pi base system?

How would you explain the act of placing quantities on symbols?

Is english your primary language and do you sometimes find yourself using difficult words or concepts that you don't entirely understand?

#### Sinny91

##### Banned

I'll post the answer tomorrow

#### Animekitty

##### baby marshmallow born today
Im sorry, i didnt make it that far in school, but it appears to me that you still havent grasp the question: In base pi how would you express this roman numeral: XIV?
logarithms

whole numbers are integers.
decimals are fractions of whole numbers.
this is why phi ratio is holistic.
any physical length can be a whole number thus phi can be the decimal of that length.
So a physical circle can become a whole number (one) and then proceed in logarithms.
14 is the ratio of 14 physical circle circumferences times pie (one).

log_pie^(n(pie))

n = 14

#### Seteleechete

##### Together forever

I'll post the answer tomorrow
It's impossible because the exit and the orb before it are both red.

#### Brontosaurie

##### Banned
What does base number of notation have to do with rationality of a number?

#### Bogart

##### Active Member
You didn't make it this far in school to learn about decimal system but you did advance enough to know about numeral systems in general which led you to asking about pi base system.
I'm tempted to look up your curriculum to confirm that decimal system is explained in the first grade of mathematics in elementary school, but I know you aren't serious.
Would you like me to go through my school history? I missed half of my sophomore year of high school and dropped out part way into my senior year when I realized I was a full year behind on credits. That has little to do with what I absorbed while I was there. I'm not sure you get it yet, but I am serious.

Decimal system is the first example of a numeral system, there's no way you haven't heard of it if you've heard of base pi and you fully understand what a numeral system or base pi mean.
I don't mean to claim I fully understand anything. I like to think of myself as a jack of all trades and a master of none.

So your argument is that arabic numerals are too coherent and therefore roman numerals should be used to allude to your point that decimal system is incompatible with the pi base system?
I think I can see where base pi could be used, but its an incomplete thought and seems to me it can only be used as comparable on subjects that are fully based on base pi, like volumes of spheres or surface areas of circles. Aside from that, Arabic numerals follow a stricter set of rules than roman numerals. In Arabic a 2s value is always 2 times the value of the location of the number in the series, but in roman numerals a V can very in value relative to its proximity to other numerals.

How would you explain the act of placing quantities on symbols?
I guess I would say it would be reducing entropy.

Is english your primary language and do you sometimes find yourself using difficult words or concepts that you don't entirely understand?
English is my primary language and I think people who are not finding themselves in conversations that contain new "words" and "concepts", at least sometimes, are not challenging themselves.

#### Bogart

##### Active Member
logarithms

whole numbers are integers.
decimals are fractions of whole numbers.
this is why phi ratio is holistic.
any physical length can be a whole number thus phi can be the decimal of that length.
So a physical circle can become a whole number (one) and then proceed in logarithms.
14 is the ratio of 14 physical circle circumferences times pie (one).

log_pie^(n(pie))

n = 14

Ah, yes, I had to look up "holistic". 14 does not have the same value in base 7 as it does in base 10. I think you are using base 10 to define base pi cycles. Honestly, I'm so lost right now, however, I have a new point I want to make about pi. I just have to find the words to do it.

#### Bogart

##### Active Member

I'll post the answer tomorrow
Schrödinger's cat didn't die for your personal pleaser, lol.

#### Blarraun

##### straightedgy
I think I can see where base pi could be used
Can't any angle, sphere or circle be used to create or mean aynthing else?
I guess I would say it would be reducing entropy.
What do you mean when saying "reducing or increasing entropy"?
English is my primary language and I think people who are not finding themselves in conversations that contain new "words" and "concepts", at least sometimes, are not challenging themselves.
Do you think you've used words or concepts you didn't entirely understand in this thread, where other, less misleading, terms could be used instead?