If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q) and (0, 0) form an equilateral triangle, then what is (p+q) equal to?

All three sides equal: distance from (0,0) to (p,1) = √(p²+1), from (0,0) to (1,q) = √(1+q²), from (p,1) to (1,q) = √((p-1)²+(1-q)²). From first two: p² = q², so p = q (both in (0,1)). Then √(p²+1) = √(2(p-1)²) needs: p²+1 = 2(p-1)² = 2p²-4p+2, so p² - 4p + 1 = 0, p = 2-√3 (taking p<1). So p+q = 2p = 4 - 2√3.