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Geometric Impossibility?? I found this puzzle online ...?
... which has me, well, puzzled! The upper image shows 4 geometric shapes within a triangle, completely filling the space. The lower image shows the same four shapes within the same triangle, but not filling the entire space. How is this possible??? The combined surface area of the four shapes has to be constant, regardless of how they are arranged, right? What am I overlooking here? Is this some kind of trick??
http://members.cox.net/natura/PUZZLEPIC.jpg
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8 Answers
- Anonymous1 decade agoFavorite Answer
is not a trick......
- 1 decade ago
Haha, I know the answer. If you look at the point in the middle of the hypotenuse of the triangle with no gap, you will see that the slopes of the lines on either side of it are not the same. In other words the upper line (hypoenuse) is bowed down to eliminate the area that is present as a gap in the lower triangle. It is extremely deceiving though.
- Anonymous1 decade ago
I do a lot of wood working were mesurements have to be exact. Get yourself a good ruller and measure the parts in the pictures as I did, you will see their not the same sizes, They very from 1/16" to as much as 1/8". If each part were the exact same size in each picture, they would fit exactly the same. I measured each part over and over again, there not the same sizes.
- astatineLv 51 decade ago
Hats off to voracious. 5/2 and 8/3 are the tans of the corresponding angles in the two triangles. his observation is great.
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- 1 decade ago
Since the green triangle has θ = arctan 2 / 5 = 21.8°,
and the red triangle has θ = arctan 3 / 8 = 20.6°,
these are not congruent, ie. the hypotenuse is not
truly straight in either diagram.
- nationsLv 44 years ago
i got here across my one and basically on line and that i'm now married to him. i think of it became into the perfect element i'd desire to have ever executed. He treats me like a queen and he has suck a loving candy heart. Oh yeah he's many years youthful too.
- 1 decade ago
It would be possible if you switch places of the yellow and the green piece... I think it's like when you put things in a box... it depends of the way you put things in.
