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Ciro Santilli (@cirosantilli, 34)

Fraction

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Reduced fraction

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A "reduced fraction" is a fraction that has the smallest possible integer numerator and denominator for its value.

For example:

\frac{3}{6}

is not a reduced fraction, because there is another fraction equal to it but with smaller numerator and denominator:

\frac{1}{2}

Farey sequence ( $F_{n}$ )

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Farey sunburst

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en.wikipedia.org/w/index.php?title=Farey_sequence&oldid=1223364653#Farey_sunburst

Number of elements in a Farey sequence

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en.wikipedia.org/w/index.php?title=Farey_sequence&oldid=1223364653#Sequence_length_and_index_of_a_fraction

∣ F_{n} ∣ = 1 + Φ (n)

where

Φ (n)

is the totient summatory function.

Numerator (Number on top)

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Denominator (Number on bottom)

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 Ancestors (6)

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