An investigation on Egyptian fractions involving algebraic proof and writing a code in python on TI Nspire to generate the fractions.
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Egyptian fractions are a fascinating topic in the history of mathematics! They are sums of distinct unit fractions, where each fraction has a numerator of 1 and a positive integer denominator.
Egyptian fractions were used by ancient Egyptian mathematicians, as seen in texts like the Rhind Mathematical Papyrus. This system was developed round 2000 BCE and was used for practical purposes such as dividing food and other resources.
No algorithms are known for producing unit fractions representations having either a minimum number of terms or smallest possible denominator. However, there are number of algorithms for decomposing an arbitrary fraction into unit fractions. In 1202, Fibonacci published an algorithm for constructing unit fractions representations, and this algorithm was subsequently discovered by Hoffman in 1998.
Greedy Algorithm: One method to find an Egyptian fraction representation is the greedy algorithm, which repeatedly subtracts the largest possible unit fraction until the remainder is zero.
