[math-fun] Triangle 1/7th of generating ABC triangle
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.
-----Original Message----- From: math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com [mailto:math-fun-bounces+andy.latto=pobox.com@mailman.xmission .com] On Behalf Of Eric Angelini Sent: Saturday, June 09, 2007 10:36 AM To: math-fun Subject: [math-fun] Triangle 1/7th of generating ABC triangle
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?
Since area and the construction are preserved under affine transformation, the answer is either "No", or "Yes, and in fact this works for every triangle ABC" Andy Latto andy.latto@Pobox.com
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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participants (3)
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Andy Latto -
Eric Angelini -
Fred lunnon