Brain teaser

[Zhuge Liang]

<div style='font: ; text-align: left; '>How is this possible?

http://www.optillusions.com/22.html

If you know the answer, don't reveal it yet. Just say whether you get it or not. We can give our answers later and compare notes.

Regards,
Zhuge Liang</div>

[ManaMan]

<div style='font: 12pt Arial; text-align: left; '>I think I might get it...</div>

[Eric]

<div style='font: 11pt ; text-align: left; '>I get it, but it's not that amazing.</div>

[Flip]

<div style='font: 12pt "Cooper Black"; text-align: left; '>I rule.

Literally, i used a ruler and found that in the top triangle the hypotnuse(sp) is bowed in while its bowed out in the bottom triangle. It must have something to do with the angle of the hypotnuses of the red and blue parts of the puzzle, i think they are different. Thus the extra square comes from that slight difference. You can tell (barely) by looking at how the hypotnuses from both the top and bottom trianlge chop off the squares of the grid. There is a slight difference that adds up to one square.</div>

[Kupek]

<div style='font: 10pt verdana; text-align: left; padding: 0% 10% 0% 10%; '>The illusion is that the green and red triangle are similar triangles. (Triangles are similar if one triangle is a "multiple" of the other - the angles are the same.)

Doing a little trig, the red triangle has angles 90, 20.556, and 69.44 degrees. The green triangle has angles 90, 21.80, and 68.2 degrees. The differences are small enough that we look at the two triangles, and assume they're similar - in fact, we've probably made such assumptions using like triangles in our geometrey textbooks, except correctly.

Since the two triangles are not similar, then the overall triangle is not truly a triangle. The "hypotenuse" is not straight. Hence, the "hole" is not really a hole, since there never was an overall triangle to begin with.</div>

[Kupek]

<div style='font: 10pt verdana; text-align: left; padding: 0% 10% 0% 10%; '>I don't think that's it. According to the text, "The partitions are exactly the same, as those used above." Read my explanation.</div>

[Zhuge Liang]

<div style='font: ; text-align: left; '>no, he's right.  you guys gave essentially the same answer...</div>

[Kupek]

<div style='font: 10pt verdana; text-align: left; padding: 0% 10% 0% 10%; '><i>Literally, i used a ruler and found that in the top triangle the hypotnuse(sp) is bowed in while its bowed out in the bottom triangle.</i>

I read that to mean that the hypotenuse of the top triangle itself was bowed in or out, which would of course mean that the top triangle is not really a triangle. I didn't realize he meant the "hypotenuse" of the whole triangle.</div>