This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different? Which
do you like best?
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
A loopy exploration of z^2+1=0 (z squared plus one) with an eye on
winding numbers. Try not to get dizzy!