# Show love for triangles

**Geometry**Level pending

In an equilateral triangle with side
length 1, consider dropping a perpendicular
from a vertex onto the
opposite side. Then, repeat this process,
spiralling in clockwise, as in the
picture. Where (**in Cartesian coordinates,
calling the bottom left vertex
the origin**) is the point to which this
process converges?

suppose the coordinates comes as \((a,b)\), submit your answer as \(a^2+b^2\) to 2 decimal places.