| Math Logic |
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| Question : |
| What
is a Farey Sequence ? |
Answer : |
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The Farey Sequence of order n is the increasing of all fractions P/q for which 0 <= p/q <= 1, q <= N, and p and q are non-negative
integers with no common divisors other than 1.
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Farey sequences are named after the British geologist John Farey.
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| The Farey sequences
of orders 1 to 5 are : |
- F1 = {0/1, 1/1}
- F2 = {0/1, 1/2,
1/1}
- F3 = {0/1, 1/3,
1/2, 2/3, 1/1}
- F4 = {0/1, 1/4,
1/3, 1/2, 2/3,
3/4, 1/1}
- F5 = {0/1, 1/5,
1/4, 1/3, 2/5,
1/2, 3/5, 2/3,
3/4, 4/5, 1/1}
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| The Farey sequence of order n contains all of
the members of the Farey sequences of lower orders. In particular Fn contains all of the members of Fn-1,
and also contains an additional fraction for each number that is less than n and coprime to n.
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