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Talk:Greedy algorithm for Egyptian fractions: Difference between revisions
Talk:Greedy algorithm for Egyptian fractions (view source)
Revision as of 18:47, 3 April 2014
, 10 years ago→Still incorrect as is: expression improper fractions with Egyptian fractions.
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(→Still incorrect as is: expression improper fractions with Egyptian fractions.) |
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The current solutions can be defended as "they match the task description", but it's better to do things right, instead of fudging the task requirement to suit existing examples. --[[User:Ledrug|Ledrug]] ([[User talk:Ledrug|talk]]) 17:43, 3 April 2014 (UTC)
: Any whole number can be expressed as a sum of 1/1 fractions, or even a vary large number of unit fractions, but that would be become voluminous with even moderate integers. The whole number part of an improper fraction (as noted in the task) are to be expressed as integers, and leave the proper fraction part to be expressed as Egyptian fractions. Egyptian fractions don't use unity as a denominator in any case, and also, Egyptian fractions must have unique denominators, so that rules out multiple 1/1 unit fractions. The inclusion of the newest part of the task wasn't meant to be a cop-out, but a practical solution to address improper fractions when expressing them in conjunction with Egyptian fractions. I read very long ago that this is the manner in which the Egyptians handled improper (or vulgar) fractions, an obvious and necessary preliminary first step. Whether or not that is thought of as a work-around, it wasn't made up just to suit existing examples, as the programming solutions were in keeping with the task's requirements. Almost all descriptions of Egyptian fractions today (from what I've viewed online) seem to assume that Egyptian fractions deal with proper fractions, and indeed, every example illustrates that assumption. Whether or not that's true, I haven't seen an example showing an Egyptian fraction example for an improper fraction. Furthermore, in all of the online calculators that convert a fraction (in particular, an improper fraction) to an Egyptian fraction, the whole part (integer) of the fraction is just shown as a simple integer followed by the Egyptian fractions, each separated by a plus sign. One reason I chose to have the whole (integer) part expressed in some manner to distinguish the whole part is that I envisioned somebody rebelling against expression the unit fractions as 1/n; some people use different notations: for instance, 8/11 as [2, 5, 37, 4070] -- most of the time without the blanks after the commas. In such a case, the (whole) integer part would need a special notation to make it clearly distinguishable from the other integers. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 18:47, 3 April 2014 (UTC)
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