Hahn distance: Difference between revisions
Wikispaces>genewardsmith **Imported revision 278341718 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 356788364 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-08-07 22:53:50 UTC</tt>.<br> | ||
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Up to the 7-limit, Hahn distance has a very nice formula give by | Up to the 7-limit, Hahn distance has a very nice formula give by | ||
||3^a 5^b 7^c||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|) | ||3^a 5^b 7^c||_hahn = (|a|+|b|+c|+|a+b+c|)/2 = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|) | ||
We may take this formula (or the similar formulas we would obtain for higher odd limits) and apply it to any triple of real numbers | We may take this formula (or the similar formulas we would obtain for higher odd limits) and apply it to any triple of real numbers | ||
||(a, b, c)||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|) | ||(a, b, c)||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|) | ||
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Up to the 7-limit, Hahn distance has a very nice formula give by<br /> | Up to the 7-limit, Hahn distance has a very nice formula give by<br /> | ||
||3^a 5^b 7^c||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|)<br /> | ||3^a 5^b 7^c||_hahn = (|a|+|b|+c|+|a+b+c|)/2 = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|)<br /> | ||
We may take this formula (or the similar formulas we would obtain for higher odd limits) and apply it to any triple of real numbers<br /> | We may take this formula (or the similar formulas we would obtain for higher odd limits) and apply it to any triple of real numbers<br /> | ||
||(a, b, c)||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|)<br /> | ||(a, b, c)||_hahn = max(|a|, |b|, |c|, |a+b|, |b+c|, |c+a|, |a+b+c|)<br /> | ||