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Math Help - Triangle Paradox

  1. #1
    Newbie Artriste's Avatar
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    Triangle Paradox

    Check out the attachment
    Attached Thumbnails Attached Thumbnails Triangle Paradox-missing.jpg  
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  2. #2
    Member
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    The title "Triangle Paradox" gives a hint: They are not triangles with or without the hole!

    Hint:

    In order for red and green triangles to line up perfectly, they must be similar triangles having the same slope. Yet they aren't.
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  3. #3
    Newbie Cooler's Avatar
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    Optical illusion

    In fact the two "triangles" are not the same size.
    The one with the hole in it is bigger.
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  4. #4
    Junior Member
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    The triangle makes use of the properties of the Fibonacci numbers. Notice that the triangle is of has sides 13 and 5 (Fibonacci). In particular it is possible to show that (Fn)^2 (the nth Fibonacci number squared) differs from F(n-1) x F(n+1) by 1 always. Sometimes + 1 sometimes - 1. The triangle you show just plays on this. Have a look at a 21 x 21 square and a 34 x 13 rectangle.
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