Tuesday, February 16, 2010

Fox 246


  1. Let the area of the smallest semi-ellipse be 1 unit and half of the full ellipse (E) be x. The area of the middle semi-ellipse is x^2. The area of the largest semi-ellipse is (1+x)^2.

    The shaded area = (1+x)^2 – 1 – x^2 = 2x, i.e. A(E).
    - Yu

  2. Yu, your solution above is a very intelligent use of similarity ratios. It was amazing that you did NOT explicitely write the formula of area of an elippse. In other words, one can solve this problem, even if s/he does not know the formula of an elippse' area. Very smart!
    Thank you.