Thread: 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.
I have attached the shape with the message.

Originally Posted by tsang

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.

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.