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Thread: Bases - Base 22/3

  1. #1 Bases - Base 22/3 
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    Aug 2014
    Just throwing a personally unchecked thought out there.

    as spheres are kind of efficient, what would maths look like if pi was to equal a whole number in a relative base?

    i.e. instead of using decimal, use base 22/3, so that PI becomes 3, and therefore no need to use the word PI

    OK I know the numbers become unmanageable without computers, but would that be a more natural base for nature, a nice whole number 3?

    If you checked out a few standard formulas, do they become cleaner in this base?

    Only a thunk....

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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Jul 2006
    pi does not equal 22/3, so it would not equal 3 in base 22/3 either. (Even 22/3 wouldn't equal 3 in base 22/3.) pi isn't even approximately 22/3. It's approximately 22/7.

    What you want is base pi, in which case pi would become 10. But numerical bases only change the way we write the number, not the number itself. pi r^2 would still be pi r^2. Besides that, writing normal numbers would become tricky. How would you write 4 in base pi? It'd need an infinite, non-repeating series of digits after the decimal now instead.

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  4. #3  
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    You mis understood.
    I think most people know pi does not equal 22/3

    Pi is generally 22/7 or 3.14 plus a load of numbers after.

    What i am suggesting is that we like base 10 because it makes sense in our 10 digit/ fingered world.
    I am asking math people or physics people how formulas would look if the relationship of surface area and volume of a circle or sphere was a whole number. 3

    Not 3.14...........

    Looking at things in a different base. Does it have any meaning.

    22/3 is 7.3333 recurring.

    If you have a base of 7.333333 recuring pi is 3

    Are there 3 quarks to an atom

    Is there a value of looking at a natural base rather than a human base.

    Now i said that it would not be easy for humans to figure such a base.

    But we have computers to crunch such numbers.

    So i would appreciate it if you vlarified questions before launching your mis aligned response.

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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    is not 3 in any base. It would be 10 in base , 100 in base and as far as anyone knows, it would not have a finite expression in nearly any other base. Since is transcendental, we know that's true for all rational bases. This is all easy to prove if you look at the definition of a numerical base.

    When you write 245.7 in base 10, that's shorthand for . If you write 323.11 in base 4, that would be . Since any rational number to an integer power is a rational number, and any finite sum or product of rational numbers is a rational number, any number with a finite representation in a rational base is a rational number. Since isn't a rational number, it can't have a finite representation in any rational base.

    3 in base 22/3 is 3. if you use the definition of a base, that expands out to .

    In base (you can use any number as a base), itself is 10, which is .

    And again, using a different base does not change the numbers. It only changes how you write them.
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  6. #5  
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    All mathematics starts with the integers. If you use anything but a (positive) integer as a basis ordinary arithmetic (like 1 + 1 = 2) would be extremely messy.
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