Egyptian fractions

I found this on Quora. What would the standard algorithm be, I wonder.
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David JoyceDavid Joyce, Professor of Mathematics at Clark Uni… (more)

Suppose you have five loaves of bread and you want to divide them evenly among seven people.  You could cut the five loaves in thirds, then you’d have 15 thirds.  Give two of them to each of the seven people.  You’ll have one third of a loaf left.  Cut it into seven equal slices and give one to each person.

\frac57=\frac13+\frac13+\frac1{21}
There may be other solutions.   a = b = 3, c = 21.   (Egyptian Fractions)

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2 Comments

Filed under arithmetic, fractions, math, operations

2 responses to “Egyptian fractions

  1. Your posts always get me thinking!
    I have nominated you for an award, and would love for you to check it out:

    https://blogcreatifa.wordpress.com/2015/03/10/liebster-award-discover-new-blogs/

  2. I like 1/2 + 1/7 + 1/14 better since it has a larger smallest piece. Nobody wants to get a pile of crumbs.

    To me the standard algorithm is the greedy one — but it can result in horrendously big denominators sometimes, and often doesn’t give a 3-fraction sum even when such a sum exists.

    There are lots of unsolved problems even in such a simple situation as this! Look up Erdos-Strauss for instance.

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