This is apparently known as "Feynman's triangle" --- see the short article at http://mysite.mweb.co.za/residents/profmd/homepage4.html Fred Lunnon On 6/9/07, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun,
Draw a triangle ABC (clockwise labels) with each side devided into 3 equal parts (labels A,A1,A2,B,B1,B2,C,C1,C2): AA1=A1A2=A2B, BB1=B1B2=B2C, CC1=C1C2=C2A.
Now draw AB1, BC1, CA1 -- those lines shape an "inside" triangle "I" having no common point with ABC.
Question: Does an ABC triangle exist such that the surface of the inner "I" triangle is exactly 1/7th of ABC's surface?
E.
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