Egyptian fraction

Every positive rational number can be represented by an Egyptian fraction.

This leather roll is an aid for computing Egyptian fractions.

These unit fractions form an Egyptian fraction representation of the number 4/n.

The modern looking multiplication and division operations had been hidden within the Egyptian fraction notation.

Therefore, the worst-case length of an Egyptian fraction of 4/n must be either three or four.

The remainder scaled Egyptian fractions to 1/320 units named ro.

An Egyptian fraction is the sum of distinct positive unit fractions, for example .

The remaining number after subtracting one of these special fractions was written using the usual Egyptian fraction representations.

The Znám problem is closely related to Egyptian fractions.

That is, they lead to an Egyptian fraction representation of the number one as a sum of unit fractions.

The value of an expression of this type is a positive rational number a/b; for instance the Egyptian fraction above sums to 43/48.

Some notable problems remain unsolved with regard to Egyptian fractions, despite considerable effort by mathematicians.

The same typical growth rate applies to the terms in expansion generated by the greedy algorithm for Egyptian fractions.

The concepts referred to in the booklet included unit fractions and Egyptian fractions.

Solutions to each problem were written out in scribal shorthand, with the final answers of all 84 problems being expressed in Egyptian fraction notation.

Fibonacci actually lists several different methods for constructing Egyptian fraction representations (, chapter II.7).

If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction.

The optimized Egyptian fraction series was an implicit topic of the RMP 2/n table.

In particular, chapter II.7 contains a list of methods for converting a vulgar fraction to an Egyptian fraction.

Such representations are popularly known as Egyptian Fractions or Unit Fractions.

The sum of the first k terms of the infinite series provides the closest possible underestimate of 1 by any k-term Egyptian fraction.

Even more strongly, for any fixed k, only a sublinear number of values of n need more than two terms in their Egyptian fraction expansions.

Egyptian fraction and base 60 monetary units were extended in use and diversity to Greek, early Islamic culture, and medieval cultures.

In number theory, the odd greedy expansion problem concerns a method for forming Egyptian fractions in which all denominators are odd.

A later text, the Rhind Mathematical Papyrus, introduced improved ways of writing Egyptian fractions.