Wednesday, March 3, 2010

Fox 258

Bleaug submitted this as the general case of a series of foxes.

3 comments:

  1. http://geometri-problemleri.blogspot.com/2010/12/problem-96-ve-cozumu.html

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  2. Same proof as number 250:
    Say base of area B is x.
    Say area D is a multiple of area B by factor k.
    Then base area D = k*x and A(D) = k^2*A(B).
    The base of area C is then x + kx = x*(k+1).
    So area C is a multiple of B by factor k+1 and A(C)=(k+1)^2*A(B).
    The shaded area = A(C)-A(B)-A(D) = ((k+1)^2-1-k^2)*A(B) = 2k*A(B).
    Area E is the result of Area(B) first horizontally stretched by factor k and then vertically multiplied by factor 2, so A(E) = A(B)*k*2 = 2k*A(B).
    QED.
    (Sorry for my poor English... I'm Dutch...)

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  3. Your proof and English are just great!
    Thank you Henkie.

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