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Math Help - Curry Triangle

  1. #1
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    Curry Triangle

    Hi, can anyone help me with this please? I want to come out with a formal proof that Curry Triangle paradox. I know the truth is that actually the side is not connected, there is slightly change on the side length. But, how can I come out with a reasonable proof? Thanks a lot.
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    Attached Thumbnails Attached Thumbnails Curry Triangle-triangle-paradix.pdf  
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  2. #2
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    Quote Originally Posted by tsang View Post
    Hi, can anyone help me with this please? I want to come out with a formal proof that Curry Triangle paradox. I know the truth is that actually the side is not connected, there is slightly change on the side length. But, how can I come out with a reasonable proof? Thanks a lot.
    I have attached the shape with the message.
    Dear tsang,

    How about the solution that is stated in wikipedia?(Missing square puzzle - Wikipedia, the free encyclopedia) I mean you can show that the ratio of sides in the blue and red traingles are not same. Hence the whole figure is an optical illusion.
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  3. #3
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    Hello, tsang!

    The Curry Triangle paradox is based on two non-similar triangles.


    The two right triangles appear to be similar (and interchangeable),
    . . but they are not.


    If they were similar right triangles, they would have a common hypotenuse.
    (Designated o - o - o - o ...)



    Code:
                                          o
                                    ..o.* |
                                ..o:::*   |3
                            ..o:::::*     |
                        ..o:::::::* - - - *
                    ..o:::::*     |   5
                 .o:::*           |3
              o:*                 |
          * - - - - - - - - - - - *
                      8

    In the first diagram, the two triangles fall below the common hypotenuse.
    Their area is short by exactly one-half a square unit.




    Code:
                                       ...o
                                 ...*:o   |
                           ...*:::o       |3
                     ...*:::::o           |
                  * - - - o - - - - - - - *
               .*:|   o            8
             .*:::o2
           .*:o   |
          o - - - *
              5

    In the second diagram, the triangle are partly above the common hypotenuse.
    Their area is over by exactly one-half a square unit.


    And that is the basis of the paradox.
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