Would Maths 'Work' in a Different Base?
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An approximation. In decimal, a few billion digits have been calculated. In hexadecimal, a representation was found.
Link or it didn't happen!
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Link or it didn't happen!
You have to wait until he makes a Wikipedia page for it... may take a second or two... :laugh:
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You have to wait until he makes a Wikipedia page for it... may take a second or two... :laugh:
If he really wants to make it convincing, he should ask for help from a pro, such as DD.
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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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An approximation. In decimal, a few billion digits have been calculated. In hexadecimal, a representation was found.
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:
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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
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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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.
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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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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He wanted a hex formula! :)
Luc Pattyn [My Articles] Nil Volentibus Arduum
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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
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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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
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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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:
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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He wanted a hex formula! :)
Luc Pattyn [My Articles] Nil Volentibus Arduum
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CP Vanity has been updated to V2.3ROTFL! Don't confuse him. :)
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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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CP Vanity has been updated to V2.3I 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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ROTFL! Don't confuse him. :)
He confuses me almost 18/7/16D.
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Luc Pattyn wrote:
do you really think you can prove your computer performs its calculations in binary arithmetic?
I'm breathing mostly empty space.
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He confuses me almost 18/7/16D.
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
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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:
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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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.