That applies to boatbuilding, the construction of an arch, ideas about natural philosophy, the uses of unit fractions, agriculture, written laws and the form of contracts, architecture, canons of proportion, and how to make beer . Rktect 01 : 03, August 27, 2005 ( UTC)
42.
In the rare case that these other methods all fail, Fibonacci suggests a greedy algorithm for computing Egyptian fractions, in which one repeatedly chooses the unit fraction with the smallest denominator that is no larger than the remaining fraction to be expanded : that is, in more modern notation, we replace a fraction " x " / " y " by the expansion
43.
The Egyptians calculated in unit fractions so to represent a number like Pi, rather than use 22 / 7 they might have represented it as 3'8'16 . . . The khet seems to be in a relation to other Egyptian units such that it facilitates calculating the area of a circular field . " Rktect 15 : 06, August 14, 2005 ( UTC)
44.
If the number is not already a unit fraction, the first method in this list is to attempt to split the numerator into a sum of divisors of the denominator; this is possible whenever the denominator is a practical number, and " Liber Abaci " includes tables of expansions of this type for the practical numbers 6, 8, 12, 20, 24, 60, and 100.
