Editing Farey sequence (section)

===Farey sunburst===
[[File:Sunburst 8.png|thumb|right|300px|Plotting ''F''<sub>6</sub> numerators vs denominators]]
[[File:Farey sunbursts 1-10.svg|thumb|right|150px|Starbursts of iterations 1–10 superimposed]]

Plotting the numerators versus the denominators of a Farey sequence gives a shape like the one to the right, shown for {{math|{{var|F}}{{sub|6}}.}}

Reflecting this shape around the diagonal and main axes generates the ''Farey sunburst'', shown below. The Farey sunburst of order {{mvar|n}} connects the visible integer grid points from the origin in the square of side {{math|2{{var|n}}}}, centered at the origin. Using [[Pick's theorem]], the area of the sunburst is {{math|4({{abs|{{var|F}}{{sub|{{var|n}}}}}} &minus; 1)}}, where {{math|{{abs|{{var|F}}{{sub|{{var|n}}}}}}}} is the [[#Sequence_length_and_index_of_a_fraction|number of fractions in {{math|{{var|F}}{{sub|{{var|n}}}}}}]].
[[File:Farey_sunburst_6.svg|thumb|center|300px|Farey sunburst of order 6, with 1 interior (red) and 96 boundary (green) points giving an area of {{math|{{color|red|1}} + {{sfrac|{{color|green|96}}|2}} − 1 {{=}} 48,}} according to [[Pick's theorem]] ]]