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Farey Starburst
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Download a Geometry Expressions Model for Farey Starburst
Farey Numbers and Kissing Circles
Take the Farey Starburst a little further with GeoGebra
Suppose you wanted to make a list of all the rational numbers between 0 and 1.
How would you start?
One approach might be to begin with the denominators of the fractions: first, list those with denominator 1 - zero and 1: \(\frac{0}{1}, \frac{1}{1} \).
Next, add those with denominator 2: \(\frac{0}{1}, \frac{1}{2}, \frac{1}{1} \).
Add those with denominator 3 ( \(\frac{0}{1}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{1}{1} \)) and you are on your way to the Farey Sequence! This last would be referred to as the Farey Sequence of Order 3.
So many patterns! So much to explore...
For example, if you plot the numerators against the denominators of a Farey Sequence, then you get the amazing Farey Starburst! (After plotting numerators against denominators, reflect in the line y = x, then reflect in both x and y axes).
Farey level 0 6 6
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