In geometric group theory, triangle groups are classified into Euclidean, spherical, and hyperbolic cases according to whether an associated sum of unit fractions is equal to one, greater than one, or less than one respectively.
32.
In Ancient Egyptian most fractions were written as the sum of two or more unit fractions ( a fraction with 1 as the numerator ), with scribes possessing tables of answers ( see Rhind Mathematical Papyrus 2 / n table ).
33.
Of these, the first is to test whether the number is itself already a unit fraction, but the second is to search for a representation of the numerator as a sum of divisors of the denominator, as described above.
34.
The decomposition of 2 / " n " into unit fractions is never more than 4 terms long as in for example 2 / 101 = 1 / 101 + 1 / 202 + 1 / 303 + 1 / 606.
35.
The Egyptians used some special notation for fractions such as \ tfrac12, \ tfrac13 and \ tfrac23 and in some texts for \ tfrac34, but other fractions were all written as unit fractions of the form \ tfrac1n or sums of such unit fractions.
36.
The Egyptians used some special notation for fractions such as \ tfrac12, \ tfrac13 and \ tfrac23 and in some texts for \ tfrac34, but other fractions were all written as unit fractions of the form \ tfrac1n or sums of such unit fractions.
37.
Describes an application of the closest approximations to one by " k "-term sums of unit fractions, in lower-bounding the number of divisors of any perfect number, and uses the same property to upper bound the size of certain groups.
38.
Reading available Middle Kingdom math records, RMP 2 / n table being one, modern students of Egyptian arithmetic may see that trained scribes improved conversions of 2 / n and n / p to concise unit fraction series by applying algorithmic and non-algorithmic methods.
39.
The frequency of the flash is adjusted so that it is an equal to, or a unit fraction of the object's cyclic speed, at which point the object is seen to be either stationary or moving slowly backward or forward, depending on the flash frequency.
40.
The St�rmer numbers arise in connection with the problem of representing the Gregory numbers ( arctangents of rational numbers ) G _ { a / b } = \ arctan \ frac { b } { a } as sums of Gregory numbers for integers ( arctangents of unit fractions ).
