A [i][color=#0000ff]lune[/color] [/i]is a [color=#0000ff][i]bidimensional surface [/i][/color]bounded by [i][color=#0000ff]two arcs[/color][/i] of a [color=#0000ff][i]circle[/i][/color] having [color=#0000ff][i]different radii[/i][/color]. [br][br][color=#0000ff][i]Hippocrates of Chios[/i][/color], the founder of the Athenian school of geometry, who lived in Athens in 450-420 a.C, was the first mathematician to study the problem of [i][color=#0000ff]squaring the lunes[/color][/i], and he showed that the [color=#0000ff][i]ratio of the areas of two circles is equal to the ratio of the squares constructed on their diameters[/i][/color].[br][br]This result is named [color=#0000ff][i]squaring [/i][/color]because it shows that a [color=#0000ff][i]curvilinear area[/i][/color] is [color=#0000ff][i]equivalent [/i][/color]to another one, [i][color=#0000ff]bounded by segments[/color][/i], so it can be easily calculated and built with compass and straightedge.[br][br]The GeoGebra applet shows a result derived from the theorem stated above.[br][br]