For the area and perimeter of a Triquetra, what is "a"? < in three overlapping circles, similar to a vesica piscis, Wolfram claims the following two equations for perimeter and area: $$perimeter = 3\pi a$$ $$area = ...--prophetes.ai

For the area and perimeter of a Triquetra, what is "a"? < in three overlapping circles, similar to a vesica piscis, Wolfram claims the following two equations for perimeter and area: $$perimeter = 3\pi a$$ $$area = \frac{1}{2}(2 \pi -\sqrt 3)a^2$$ Which are straight forward enough, except they don't explain what "a" is. I am guessing "a" is the distance from two intersections on any 'petal' of this 3 petaled leaf, but I could be wrong.

$a$ is clearly intended to be the radius of the circles it is constructed from. The distance between intersections is the radius of the circles. Each arc of the circumference is $\frac 16$ of a circle, so the perimeter should be $2\pi a$. I would send an e-mail alerting mathworld to the typo. You could check the area calculation to confirm this or to alert them to a problem there as well.