Two nonnegative reduced fractions and make a Farey pair (with ) whenever , in other words, they are a Farey pair if their difference is . The interval is known as a Farey interval.
Given a Farey pair , their mediant is . The mediant has the following property:
If is a Farey interval, then the two subintervals obtained when inserting the mediant are also Farey pairs. Besides, between all fractions that are strictly between , the mediant is the one having the smallest denominator.
Notice that and form a Farey pair, since . The mediant here is .
Then and form a Farey pair: . No fraction between and other than has a denominator smaller or equal than .
|Date of creation||2013-03-22 14:54:42|
|Last modified on||2013-03-22 14:54:42|
|Last modified by||drini (3)|