I presume we use the 10 base system because weve got 10 fingers. Imagine if we were like the simpsons and only had 8 fingers.
Using a 22 base, obviously Pi would be 7.........have I answered my own question? or am i just stupid? (no answer needed for that bit thanks)
2006-09-21 00:27:06 · 8 answers · asked by Old Cynic 3 in Science & Mathematics ➔ Mathematics
Forget whole numbers . you cannot even get in recurring decimal. To prove if it is recurring decimal in say base x and it reccurs afer m digit with a frequecny of n(say base b)
a x1 x2 etc are digits so is a1 a2 etc
pi = a.x1x2.... xm a1a2a3... an a1 a2 a3....an
then pi*b^m = ax1x2....xm . a1a2... an.a1a2...an......
pi*b^m^b^n = ax1.....xma1....an.a1....an...
subtract the two
pi*b^m(b^n-1) = integer
or pi *integer = integer
pi is rational which is contradiction
so it cannot be done to a rational base. It can be done to irrational base
= 10 to base pi
2006-09-21 01:17:02 · answer #1 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
No, using a base 22, Pi would still start with a 3. The base only determines when the shift to next column occurs from the decimal place (that is, in base 22, writing "10" would be 22, adn "11" would be 23. But any value less than our 10 would still be written the same, unless you insist on changing the symbols. If you work with computerts, you can get familiar with the hexadecimal system, which counts 0, 1, 2 ... 9, A, B, C, D, E, F, 11, 12 ...). In hexadecimal (base 16) 3 is still written 3.
And no, even in a different base, Pi would still be an irrational number. Shifting base is a rational operation, and rational operations will not make an irrational number rational.
2006-09-21 07:35:21 · answer #2 · answered by Vincent G 7 · 1⤊ 0⤋
No.
And the old 22/7 fraction does not accurately represent pi, it's simply as close as one can simplistically come to doing it through use of a fraction.
2006-09-21 07:37:46 · answer #3 · answered by m.allen 4 · 0⤊ 0⤋
The rationality or irrationality of a number is independent of its base notation.
If you represented pi in a hypothetical pi notation base, it would be represented as 10, but pi would still be irrational. (Unfortunately, base notation is only defined for integer base numbers.)
Your idea is brilliant, but unfortunately wrong.
2006-09-21 09:53:39 · answer #4 · answered by Deep Thought 5 · 0⤊ 0⤋
22/7 is larger than Pi.
The only possible system would be a Pi-based system and I'm all for it! Yummie!
2006-09-21 07:30:57 · answer #5 · answered by OMG, I ♥ PONIES!!1 7 · 0⤊ 0⤋
unfortunately no, and you can't square a circle and the diagonal of a square is still not measurable in the same units as its sides. These are all geometrics and are not number dependent.
2006-09-21 08:04:30 · answer #6 · answered by Anonymous · 1⤊ 0⤋
That is a wonderful, creative question. Good thinking!
2006-09-21 07:29:22 · answer #7 · answered by Anonymous · 0⤊ 1⤋
No.
2006-09-21 07:35:45 · answer #8 · answered by Redeemer 5 · 0⤊ 0⤋