Would Maths 'Work' in a Different Base?
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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
The quality and detail of your question reflects on the effectiveness of the help you are likely to get.
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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.
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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.
I never said it became finite.
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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
Mathematics is not a science of numbers, but rather a science of the relationships among numbers. In fact, it can be boiled down to relationships, period. Numbers happen to work well as a common coin, but mathematics works as well for notes in a musical scale. You can rotate, translate, change base, or work with the hyperbolic cosine of the symbolic representation of a relationship, and it will all work out the same. But you might be making it a lot harder for yourself. A change of base is often used to make a job easier to do, without changing the underlying principle. Try building a decimal computer some time. It can be done, but it can't be done conveniently or cheaply, as a device that can operate on ten states is a lot more complex and expensive than one which is stable in only two states. The result is that we have binary computers for economic reasons. As programmers, we use hex and octal representations sometimes, but that's to make our jobs easier on our brains; the computer will always translate our products into binary before processing it, then it will change base again to make the result easier for us to understand. The math remains the same.
Will Rogers never met me.
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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
Benjamin Breeg wrote:
Does Riemann's hypothesis work in any base?
Yes. The numbers themselves aren't base 10; we just use base 10 to communicate with each other about them.
I wanna be a eunuchs developer! Pass me a bread knife!
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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 don't see why not. Surely the base is just the way that the number is written down and doesn't change any of the calculations etc?
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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