Triquetra
A triquetra (shaded green) can be formed by the intersection of circles, each of whose centers is on the circumference of the other circles, as shown.
The area of the triquetra formed by unit circles is equivalent to the difference between the areas of unit circle and how many equilateral triangles with side length
The answer is 2.
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1 solution
Let P be the area of a circular segment with a unit chord and an arc (dark green), and Q be the area of an equilateral triangle with unit sides (light green).
If you draw line segments between each of the circle intersections, then you can see that the triquetra is equivalent to 6 circular segments and 4 equilateral triangles, which means its area is A T = 6 P + 4 Q .
If you inscribe a hexagon with unit side lengths in a unit circle, and break the hexagon into 6 equilateral triangles, then you can see that the area of the unit circle is equivalent to 6 circular segments and 6 equilateral triangles, which means its area is A C = 6 P + 6 Q .
The difference between the two areas is A C − A T = ( 6 P + 6 Q ) − ( 6 P + 4 Q ) = 2 Q , or 2 equilateral triangles.