That's part of the illusion. It's supposed to look like a 5-12-13 right triangle, but the 2 smaller triangles aren't perfect fits since they forced breaks at the grid lines. Adding up the component pieces is 32 sq units, but the proper 5-12-13 triangle would be 30 sq units.
Well, shit. I passed on blabbing about this over on the Book Of Farce, only to find that I've been beaten to the punch over here. :-)
Of course, one could answer 'From where comes this "hole"?' with 'A lot of rimming and an increasing number of well-lubed fingers.' Well, that's how it works on me...
correct... the red triangle grows at 3/8ths pace = 0.375, the teal triangle grows at 2/5ths pace = 0.4, thus making the upper combined "slope" concave (having white space) wrt. the end points whilst the lower slope is actually convex (wrt. end points)
The area of the hole at the bottom is actually the area of the white space under the line of the end points in the upper figure plus the area that is above said line of the lower figure ;-D
All gay men should know the CORRECT answer! When the square is sitting next to the red triangle, it's harder to see, because wearing red is slimming...
The two triangles have different slopes. In the lower arrangement, the hypotenuse is bowed outward, compared to inward above the slight difference in area is the rough equivalent of one square on the grid.
I don't think any of these answers are correct. Note that the same two shapes are always on top. If two good tops can't find one little hole, then what's the world coming to?
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no subject
Date: 2010-11-22 08:54 pm (UTC)no subject
Date: 2010-11-22 09:02 pm (UTC)The hypotenuse, the long side, isn't quite straight in either. In the top one it bows in a bit, in the bottom it bows out a bit.
The smartass who thought of it is using the fact that Fibonacci numbers and the golden ratio are linked.
http://en.wikipedia.org/wiki/Golden_ratio#Relationship_to_Fibonacci_sequence
The slope of the hypotenuse of all the triangles is close enough to 1/phi^2 that it fools the eye.
no subject
Date: 2010-11-22 09:12 pm (UTC)no subject
Date: 2010-11-22 09:14 pm (UTC)Of course, one could answer 'From where comes this "hole"?' with 'A lot of rimming and an increasing number of well-lubed fingers.' Well, that's how it works on me...
no subject
Date: 2010-11-22 10:06 pm (UTC)the red triangle grows at 3/8ths pace = 0.375, the teal triangle grows at 2/5ths pace = 0.4, thus making the upper combined "slope" concave (having white space) wrt. the end points whilst the lower slope is actually convex (wrt. end points)
The area of the hole at the bottom is actually the area of the white space under the line of the end points in the upper figure plus the area that is above said line of the lower figure ;-D
no subject
Date: 2010-11-22 11:37 pm (UTC)no subject
Date: 2010-11-23 01:29 am (UTC)no subject
Date: 2010-11-23 02:56 pm (UTC)no subject
Date: 2010-11-23 06:35 pm (UTC)