Egyptian Fractions

10 hours ago

Egyptian fraction representation uses sums of distinct unit fractions.
The greedy algorithm often yields suboptimal expansions, like 2/9 = [5,45] but better as [6,18].
Fractions like 19/20 can be inefficiently expressed, e.g., [2,3,9,180] instead of simpler forms.
Ahmes' table for fractions of the form 2/n alone suffices to compute all rational numbers, eliminating need for separate tables like 3/n.
Alternative methods include expanding numerators as powers of 2, leveraging known Egyptian arithmetic.
Creating the 2/n table requires complex searching and number theory, but once built, it enables trivial computation of any division problem.

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