For s in [0,1], define an s-median of a triangle (ABC in counterclockwise order) from vertex A to be the line segment connecting A to the point P of the opposite side BC such that BP : PC = s : (1-s) . (E.g., an ordinary median is a (1/2)-median.) A / \ / \ / \ / \ / \ B------P---------C Old math puzzle: Suppose we draw all three s-medians of an equilateral triangle ABC, where s = 1/3. Let delta be the triangle bounded by segments of the three s-medians. Find the ratio area(delta) / area(ABC). New math puzzle: Suppose we draw the r-, s- and t-medians of an equilateral triangle ABC for r, s, t in [0,1], again assuming ABC go counterclockwise around the perimeter. Let delta be the triangle bounded by segments of the three "medians". Find the ratio area(delta) / area(ABC) . ——Dan