Taxicab distance
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2011-09-03 04:00:47 UTC.
- The original revision id was 250467458.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. To calculate the number of prime factors in a [[monzo]], simply take sum of the absolute values of each coordinate. For example, 81/80 i.e. |-4 4 1> would have a factor limit of 4+4+1=9, or, with 2's taken for granted, 4+1=5. =Not yet the right name= I want to speak of a limit on the number of instances of prime factors, not the number of different prime factors. For example, 45 has factors 3, 3, and 5; here, we want to count each 3 separately. =With 2's taken for granted= ==2-factor-limit commas== 16/15 (3 * 5) 21/20 (3 * 7) 33/32 (3 * 11) 65/64 (5 * 13) ==3-factor-limit commas== 25/24 (5 * 5 / 3) 128/125 (5 * 5 * 5) 26/25 (13 / 5 / 5) 49/48 (7 * 7 / 3) 64/63 ( / 3 / 7 / 7) 256/245 ( / 5 / 7 / 7) 80/77 (5 / 7 / 11) 22/21 (11 / 3 / 7) 40/39 (5 / 3 / 13) 96/91 (3 / 7 / 13) 55/52 (5 * 11 / 13) 1024/1001 (7 * 11 * 13) 512/507 (3 * 13 * 13) 169/160 (13 * 13 / 5) 176/169 (11 / 13 / 13)
Original HTML content:
<html><head><title>commas by taxicab distance</title></head><body>One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude.<br /> <br /> To calculate the number of prime factors in a <a class="wiki_link" href="/monzo">monzo</a>, simply take sum of the absolute values of each coordinate.<br /> <br /> For example, 81/80 i.e. |-4 4 1> would have a factor limit of 4+4+1=9, or, with 2's taken for granted, 4+1=5.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Not yet the right name"></a><!-- ws:end:WikiTextHeadingRule:0 -->Not yet the right name</h1> I want to speak of a limit on the number of instances of prime factors, not the number of different prime factors. For example, 45 has factors 3, 3, and 5; here, we want to count each 3 separately.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="With 2's taken for granted"></a><!-- ws:end:WikiTextHeadingRule:2 -->With 2's taken for granted</h1> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="With 2's taken for granted-2-factor-limit commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->2-factor-limit commas</h2> 16/15 (3 * 5)<br /> 21/20 (3 * 7)<br /> 33/32 (3 * 11)<br /> 65/64 (5 * 13)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="With 2's taken for granted-3-factor-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->3-factor-limit commas</h2> 25/24 (5 * 5 / 3)<br /> 128/125 (5 * 5 * 5)<br /> 26/25 (13 / 5 / 5)<br /> 49/48 (7 * 7 / 3)<br /> 64/63 ( / 3 / 7 / 7)<br /> 256/245 ( / 5 / 7 / 7)<br /> 80/77 (5 / 7 / 11)<br /> 22/21 (11 / 3 / 7)<br /> 40/39 (5 / 3 / 13)<br /> 96/91 (3 / 7 / 13)<br /> 55/52 (5 * 11 / 13)<br /> 1024/1001 (7 * 11 * 13)<br /> 512/507 (3 * 13 * 13)<br /> 169/160 (13 * 13 / 5)<br /> 176/169 (11 / 13 / 13)</body></html>