## Saturday, 24 September 2011

### How Can This Be True?

If the partitions are the same, shouldn't every space be filled?

1. Nope. The Yellow shape is longer than the green, therefore making the whole. It's like playing tetris.

1. yes, but if you think about the equasions used to figure out surface area, the shape is the same dimensions but doesnt have the equivelant surface area, therefore making the image impossible, i just created it out of paper and it still works, i dont know how to explain how... it just does

2. the red area in lower part has one block less than the upper part thats why one block has left

3. Your eyes think they are looking at the area of a triangle: Area = 1/2 base * height = 1/2*12*5 = 30 units.
However , the top is actually a convex and the bottom a concave 4-sided polygon. The slope of the red and green triangles are not the same.

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4. the key to understand the trick is that both the 'triangle' is not a triangle.. then u can find the answer.. ;))

5. look where the orange is placed and ull see it

6. if u go more deep its because of the area occupied both the triangles are different and due to the shifting of the the triangle the total all blocks together occupies more area in second image which leads to an empty box

7. In short, both the top and bottom figures are not triangles. The top is a quadrilateral and the bottom is a quadrilateral with a small square cut out. :)

In the top figure, what is thought of as a the hypotenuse of the "triangle" is in fact made up of 2 lines of different gradient (slope), hence forming a very shallow "v" and not a straight line!.

In the bottom figure, the perceived "hypotenuse" of the "triangle" is actually a bulge (opposite of a "v").

If you overlap the top and bottom figure, the area formed by the bulge in the bottom figure and the "v" in the top figure will be exactly equal to the area of the "missing" square. This accounts for the "missing square".

I have published my explanation here =D