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.