Delta-N ratio: Difference between revisions
m changed \frac to \dfrac at the start of the article to make the fractions possibly more readable, the formula being basically a display-style there |
m →Properties: yet another minor clarification |
||
| Line 77: | Line 77: | ||
* 4/1 = (12/9) (9/6) (6/3) = '''(4/3) (3/2) (2/1)''' ''— now we can’t get delta-3 because there are 3 factors.'' | * 4/1 = (12/9) (9/6) (6/3) = '''(4/3) (3/2) (2/1)''' ''— now we can’t get delta-3 because there are 3 factors.'' | ||
* 4/1 = (16/13) (13/10) (10/7) (7/4). | * 4/1 = (16/13) (13/10) (10/7) (7/4). | ||
Also, if you factorize like this into ''K'' factors, then each of them into ''L'' factors, you get the same as if you directly factored into ''K L'' factors. | Also, if you factorize like this into ''K'' factors, then each of them into ''L'' factors, you get the same as if you directly factored into ''K L'' factors (including their order). | ||
:''The general formula for this factorization is <math>\prod\limits_{i = 1}^K \frac {K A + i N} {K A + (i - 1) N} = \frac {A + N} A</math>. Here you can see more clearly that actual delta of factors will be <math>N / \operatorname{gcd}(K, N)</math>.'' | :''The general formula for this factorization is <math>\prod\limits_{i = 1}^K \frac {K A + i N} {K A + (i - 1) N} = \frac {A + N} A</math>. Here you can see more clearly that actual delta of factors will be <math>N / \operatorname{gcd}(K, N)</math>.'' | ||