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  3. Would Maths 'Work' in a Different Base?

Would Maths 'Work' in a Different Base?

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  • A Albert Holguin

    You have to wait until he makes a Wikipedia page for it... may take a second or two... :laugh:

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    AspDotNetDev
    wrote on last edited by
    #16

    If he really wants to make it convincing, he should ask for help from a pro, such as DD.

    [Managing Your JavaScript Library in ASP.NET]

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    • B Bassam Abdul Baki

      For the most part, yes. There are some things that work in some bases, but not in others, even in some complex bases. A hexadecimal representation of pi was discovered a while back, but no decimal representation is possible (I think).

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      Luc Pattyn
      wrote on last edited by
      #17

      You probably mean 16/7. It is too bad there is no Nobel prize for Maths. :((

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      • B Bassam Abdul Baki

        An approximation. In decimal, a few billion digits have been calculated. In hexadecimal, a representation was found.

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        AspDotNetDev
        wrote on last edited by
        #18

        If you are talking about this, it just allows you to calculate the n-th digit of pi in a variety of number bases, but the number of digits is still infinite. Well, unless your number system is in increments of pi (0π, 1π, 2π...). :rolleyes:

        [Managing Your JavaScript Library in ASP.NET]

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        • B Ben Breeg

          So there I was, wallowing in the bath when it suddenly occurs to me 'would maths work the same if we used a different base.' What I mean is, lets say instead of the 10 fingers that we have and on which our decimal counting system is based we had say 14 fingers so we would be counting in base 14 as the norm. Would things like Pythagoras theorem, the Fibonacci sequence, Pi, prime numbers, calculus, square roots, sins, cosines and tangents work? Not being a mathematician, I can't get my head round whether these would work or not. Intuition tells me it would. Would this work in base 14? http://news.bbc.co.uk/1/hi/sci/tech/2911945.stm[^] Does Riemann's hypothesis work in any base? What do the great and good think?

          I am the Breeg, goo goo g'joob Aici zace un om despre care nu sestie prea mult

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          Amar Chaudhary
          wrote on last edited by
          #19

          It would have evolved that way - they didn't have borrowed characters form alphabets. And its not about conversion from based 10 to base x, everything would have been developed according to base x, so there is a probability that they would have figured out something similar but can't be said exactly....

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          • G Gregory Gadow

            Yes and no. With sequences of whole numbers, base does not matter. However, some properties of a sequence, such as the "shallow diagonal" property of the Fibonacci sequence, take on different characteristics in different bases. Geometric values, such as pi, phi and e, will be eqivalent regardless of base: given any circle, the ratio of its circumference and its diameter will equal pi regardless of what base you are using. The most notable problem when using different bases is the representation of a fractional part. For example, the ratio of 1/10 in base-10 evaluates to a rational number, 0.1. The eqivalent in base-2, 1/1010, evaluates to an irrational number, 0.000110011.... There is a whole branch of mathematics that looks at translation between bases, although I cannot remember what that field is.

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            Sean Cundiff
            wrote on last edited by
            #20

            Gregory.Gadow wrote:

            The most notable problem when using different bases is the representation of a fractional part. For example, the ratio of 1/10 in base-10 evaluates to a rational number, 0.1. The eqivalent in base-2, 1/1010, evaluates to an irrational number, 0.000110011....

            Actually, the base of a number has nothing to do with whether it's rational or irrational. Your example of 1/10 in base-2 is still rational as a rational number is a number that can be represented by: P/Q Where P and Q are integers. In base-10 your example is 1/10. In base-2 your example is 1/1010. Both are the ratio of two integers and thus are rational. Don't confuse a decimal fraction that is infinitely long as irrational. 1/3 is a rational number yet its decimal representation is 0.3333333... If the decimal fraction is finite length the number is rational. If the decimal fraction is infinite length but repeating the number is rational. If the decimal fraction is infinite length and non-repeating the number is irrational.

            -Sean ---- Fire Nuts

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            • L Luc Pattyn

              You probably mean 16/7. It is too bad there is no Nobel prize for Maths. :((

              Luc Pattyn [My Articles] Nil Volentibus Arduum

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              AspDotNetDev
              wrote on last edited by
              #21

              Luc Pattyn wrote:

              You probably mean 16/7.

              :confused:

              [Managing Your JavaScript Library in ASP.NET]

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              • A AspDotNetDev

                Luc Pattyn wrote:

                You probably mean 16/7.

                :confused:

                [Managing Your JavaScript Library in ASP.NET]

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                Luc Pattyn
                wrote on last edited by
                #22

                He wanted a hex formula! :)

                Luc Pattyn [My Articles] Nil Volentibus Arduum

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                • S Sean Cundiff

                  Gregory.Gadow wrote:

                  The most notable problem when using different bases is the representation of a fractional part. For example, the ratio of 1/10 in base-10 evaluates to a rational number, 0.1. The eqivalent in base-2, 1/1010, evaluates to an irrational number, 0.000110011....

                  Actually, the base of a number has nothing to do with whether it's rational or irrational. Your example of 1/10 in base-2 is still rational as a rational number is a number that can be represented by: P/Q Where P and Q are integers. In base-10 your example is 1/10. In base-2 your example is 1/1010. Both are the ratio of two integers and thus are rational. Don't confuse a decimal fraction that is infinitely long as irrational. 1/3 is a rational number yet its decimal representation is 0.3333333... If the decimal fraction is finite length the number is rational. If the decimal fraction is infinite length but repeating the number is rational. If the decimal fraction is infinite length and non-repeating the number is irrational.

                  -Sean ---- Fire Nuts

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                  Gregory Gadow
                  wrote on last edited by
                  #23

                  D'oh! That's embarassing. Yes, I meant to say "finite" for base-10 and "infinite" for base-2. As a former math major, I should have known better.

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                  • B Ben Breeg

                    So there I was, wallowing in the bath when it suddenly occurs to me 'would maths work the same if we used a different base.' What I mean is, lets say instead of the 10 fingers that we have and on which our decimal counting system is based we had say 14 fingers so we would be counting in base 14 as the norm. Would things like Pythagoras theorem, the Fibonacci sequence, Pi, prime numbers, calculus, square roots, sins, cosines and tangents work? Not being a mathematician, I can't get my head round whether these would work or not. Intuition tells me it would. Would this work in base 14? http://news.bbc.co.uk/1/hi/sci/tech/2911945.stm[^] Does Riemann's hypothesis work in any base? What do the great and good think?

                    I am the Breeg, goo goo g'joob Aici zace un om despre care nu sestie prea mult

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                    Soulus83
                    wrote on last edited by
                    #24

                    I remember having read that a lot of common problems and complication of decimal system would be non-existent if we used duodecimal system.... Clickety!

                    "Whether you think you can, or you think you can't--either way, you are right." — Henry Ford "When I waste my time, I only use the best, Code Project...don't leave home without it." — Slacker007

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                    • A AspDotNetDev

                      If you are talking about this, it just allows you to calculate the n-th digit of pi in a variety of number bases, but the number of digits is still infinite. Well, unless your number system is in increments of pi (0π, 1π, 2π...). :rolleyes:

                      [Managing Your JavaScript Library in ASP.NET]

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                      Bassam Abdul Baki
                      wrote on last edited by
                      #25

                      That's the one. In base 10, you need to calculate all n digits to calculate the (n+1)th. With that equation, you calculate the nth in base 16 (or 2) without having to calculate the previous ones. Some things are unique to some bases.

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                      • L Luc Pattyn

                        He wanted a hex formula! :)

                        Luc Pattyn [My Articles] Nil Volentibus Arduum

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                        Bassam Abdul Baki
                        wrote on last edited by
                        #26

                        ROTFL! Don't confuse him. :)

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                        • L Luc Pattyn

                          You probably mean 16/7. It is too bad there is no Nobel prize for Maths. :((

                          Luc Pattyn [My Articles] Nil Volentibus Arduum

                          The quality and detail of your question reflects on the effectiveness of the help you are likely to get.
                          Please use <PRE> tags for code snippets, they improve readability.
                          CP Vanity has been updated to V2.3

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                          Bassam Abdul Baki
                          wrote on last edited by
                          #27

                          I wonder if that adage about a mathematician sleeping with Nobel's wife is true? If so, he got the first and main prize.

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                          • B Bassam Abdul Baki

                            ROTFL! Don't confuse him. :)

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                            AspDotNetDev
                            wrote on last edited by
                            #28

                            He confuses me almost 18/7/16D.

                            [Managing Your JavaScript Library in ASP.NET]

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                            • A AspDotNetDev

                              Luc Pattyn wrote:

                              do you really think you can prove your computer performs its calculations in binary arithmetic?

                              You think that's air you're breathing?

                              [Managing Your JavaScript Library in ASP.NET]

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                              PIEBALDconsult
                              wrote on last edited by
                              #29

                              I'm breathing mostly empty space.

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                              • A AspDotNetDev

                                He confuses me almost 18/7/16D.

                                [Managing Your JavaScript Library in ASP.NET]

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                                Luc Pattyn
                                wrote on last edited by
                                #30

                                You're fortunate, next year will leap. Not sure yet whether you'll get a day without confusion, or just a bonus. :)

                                Luc Pattyn [My Articles] Nil Volentibus Arduum

                                The quality and detail of your question reflects on the effectiveness of the help you are likely to get.
                                Please use <PRE> tags for code snippets, they improve readability.
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                                • B Bassam Abdul Baki

                                  For the most part, yes. There are some things that work in some bases, but not in others, even in some complex bases. A hexadecimal representation of pi was discovered a while back, but no decimal representation is possible (I think).

                                  Web - BM - RSS - Math - LinkedIn

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                                  Dan Neely
                                  wrote on last edited by
                                  #31

                                  Bassam Abdul-Baki wrote:

                                  A hexadecimal representation of pi was discovered a while back, but no decimal representation is possible (I think).

                                  Nope. Either your memory, or the person who told you that is mistaken. Pi is an Irrational number[^], which means it's been proven to be impossible to write in the form a/b; which makes it infinite and non-repeating in any base.

                                  3x12=36 2x12=24 1x12=12 0x12=18

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                                  • D Dan Neely

                                    Bassam Abdul-Baki wrote:

                                    A hexadecimal representation of pi was discovered a while back, but no decimal representation is possible (I think).

                                    Nope. Either your memory, or the person who told you that is mistaken. Pi is an Irrational number[^], which means it's been proven to be impossible to write in the form a/b; which makes it infinite and non-repeating in any base.

                                    3x12=36 2x12=24 1x12=12 0x12=18

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                                    Bassam Abdul Baki
                                    wrote on last edited by
                                    #32

                                    According to this[^], "For centuries it had been assumed that there was no way to compute the _n_th digit of π without calculating all of the preceding n − 1 digits."

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                                    • B Bassam Abdul Baki

                                      According to this[^], "For centuries it had been assumed that there was no way to compute the _n_th digit of π without calculating all of the preceding n − 1 digits."

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                                      AspDotNetDev
                                      wrote on last edited by
                                      #33

                                      There are still an infinite number of digits; it's just that in base-16 any one of those digits can be calculated without calculating the others.

                                      [Managing Your JavaScript Library in ASP.NET]

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                                      • A AspDotNetDev

                                        There are still an infinite number of digits; it's just that in base-16 any one of those digits can be calculated without calculating the others.

                                        [Managing Your JavaScript Library in ASP.NET]

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                                        Bassam Abdul Baki
                                        wrote on last edited by
                                        #34

                                        I never said it became finite.

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                                        • B Bassam Abdul Baki

                                          According to this[^], "For centuries it had been assumed that there was no way to compute the _n_th digit of π without calculating all of the preceding n − 1 digits."

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                                          Dan Neely
                                          wrote on last edited by
                                          #35

                                          Other than (arguably) being prettier, there's nothing to make that representation better than any of the other formulas.

                                          3x12=36 2x12=24 1x12=12 0x12=18

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