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Talk:Greedy algorithm for Egyptian fractions: Difference between revisions
Talk:Greedy algorithm for Egyptian fractions (view source)
Revision as of 21:56, 7 June 2018
, 5 years ago→Rename and rewrite task as "Greedy algorithm for Egyptian fractions": new section
m (→Request for task clarification: corrected a typo.) |
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: Visibility of formulae to Chrome, IE/Edge, Safari etc restored by reverting task description to state before under-tested cosmetic edits of 02:50, 16 August 2016. The editor may wish to restore some of these cosmetic edits, testing their real effects in Google, Microsoft and Apple's browsers, but the the most practical immediate solution is simply to return to the state before visibility of formulae was lost. [[User:Hout|Hout]] ([[User talk:Hout|talk]]) 00:29, 17 October 2016 (UTC)
== Rename and rewrite task as "Greedy algorithm for Egyptian fractions" ==
This task is (and should be) about
[[wp:Greedy_algorithm_for_Egyptian_fractions|the greedy Egyptian expansion]]
and not about
[[wp:Egyptian_fraction|Egyptian fractions]].
Above, [[User:Gerard Schildberger|Gerard Schildberger]] wrote:
: > "Whether or not that's true, I haven't seen an example showing an Egyptian fraction example for an improper fraction."
[[wp:Egyptian_fraction#Motivating_applications|Wikipedia]] has an example, namely: 13/12 = 1/2 + 1/3 + 1/4.
Furthermore, that Wikipedia page covers several calculation methods and shows a "much better expansion" (their words) for 5/121 = 1/33 + 1/121 + 1/363.
The task currently says:
:* show '''''the''''' Egyptian fractions for: <math> \tfrac{43}{48} </math> and <math> \tfrac{5}{121} </math> and <math> \tfrac{2014}{59} </math>
but as shown above there is not a unique Egyptian fraction for a given positive rational number.
I think this task should be renamed and rewritten to be only about the narrower [[wp:Greedy_algorithm_for_Egyptian_fractions|Greedy algorithm for Egyptian fractions]],
and only for proper fractions.
A more general task about Egyptian fractions (if desired) should probably encourage giving the "better" expansions by using other/multiple methods.
The task also currently says:
:* '''for all''' proper fractions, <math>\tfrac{a}{b}</math> where <math>a</math> and <math>b</math> are positive one-or two-digit (decimal) integers, '''find and show an''' Egyptian fraction that has:
::* the largest number of terms,
::* the largest denominator.
Since a given number can have multiple valid Egyptian fraction expansions, as written, the task seems to imply you want output for each proper fraction the results of a search through all possible expansions looking for large number of terms and large denominators.
Existing solutions (mostly) instead calculate the greedy Egyptian expansion for each proper fraction looking for the largest number of terms and largest denominator.
This should be what the rewritten task actually asks for.
—[[User:dchapes|dchapes]] ([[User talk:dchapes|talk]] | [[Special:Contributions/dchapes|contribs]]) 21:56, 7 June 2018 (UTC)
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