- #1
Chrono G. Xay
- 92
- 3
Would it be possible to write an equation utilizing a summation of a modular function of a Cartesian function, whose degree is dependent upon the index of the root, in that it predicts the digits less than 1 of the root, that when summed equals the computed value sqrt( n )?
I already have what feels like a basis upon which to start,
[Summation; x=1, (inf)] \frac{(integer(f(x))mod10)}{10x}
in that it would return such values as...
0.1 + 0.02 + 0.003 + 0.0004
but am having trouble coming up with an algorithm which would strip away, for example, the 1.0 from 1.732... in sqrt( 3 ) .
It seems as though even if such a thing were doable, it would have been nice to be able to say that, with the appropriate formulae for f(x), for one, it could compute the digits of any irrational number, except that for non-root irrational numbers, such as e, θ, φ, etc. the index is arguably one (given π is obtained from a quotient, and e is obtained from the limit of an exponential...)[/sup]
I already have what feels like a basis upon which to start,
[Summation; x=1, (inf)] \frac{(integer(f(x))mod10)}{10x}
in that it would return such values as...
0.1 + 0.02 + 0.003 + 0.0004
but am having trouble coming up with an algorithm which would strip away, for example, the 1.0 from 1.732... in sqrt( 3 ) .
It seems as though even if such a thing were doable, it would have been nice to be able to say that, with the appropriate formulae for f(x), for one, it could compute the digits of any irrational number, except that for non-root irrational numbers, such as e, θ, φ, etc. the index is arguably one (given π is obtained from a quotient, and e is obtained from the limit of an exponential...)[/sup]
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