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I recently read about the study of Egyptian Fractions on the Good Math, Bad Math blog. The references to this article show that many years of research have gone into trying to find efficient ways to calculate the minimum length forms.

Are there any real-world applications that computing minimum-length Egyptian forms can be applied to?

Jen S.
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    The Wikipedia link you gave includes some applications. In particular I would say that https://en.wikipedia.org/wiki/Egyptian_fraction#Equally_distributing_objects is a reasonable real-world application. – mathmandan Feb 17 '15 at 07:17
  • Good point. However, is this really the way certain products or algorithms work? Is this method used in electronics or computation somehow? Is there a business or public institution somewhere that finds the advances in minimum-length Egyptian fractions beneficial? – Jen S. Feb 17 '15 at 09:24

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Electronic circuit design is one area where Egyptian fractions have practical use. When electrical resistors are added to a parallel circuit, the reciprocals are added to find the total resistance. An example is a parallel circuit with 1,2,3, and 6 Ohm resistors.

$$\frac{2}{1\Omega}=\frac{1}{1\Omega}+\frac{1}{2\Omega}+\frac{1}{3\Omega}+\frac{1}{6\Omega}$$

Inductance (L) in Henrys (H) in parallel circuits is calculated in the same way.

$$\frac{1}{2 H}=\frac{1}{4 H}+\frac{1}{5 H}+\frac{1}{36 H}+\frac{1}{45 H}$$

KYZYL
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