A No Nonsense Blog

4 Responses to WTF?! Someone Explain

1. Aditya September 2, 2008 at 8:17 pm

   Draw it on a piece of paper, cut the pieces, rearrange and tell me, what do you see? Then we will research a bit more on this.

   Reply
2. Sandeep September 2, 2008 at 9:04 pm

   @Aditya: yeah noticed

   Still think its awesome

   Reply
3. Ken September 5, 2008 at 9:23 am

   Notice that the slope of the hypotenuse of the red triangle and the blue triangle are different. So if you draw a straight line from point A to point B on the top picture, you will find that the line will lie outside the profile of the entire shape. This difference between the profile of the shape and the straight line form an imaginary triangle with an area exactly half the area of the missing square in the bottom picture. Now if you draw that same straight line from point A to point B on the bottom picture, you will find it intersects the profile of the entire shape. The area of this intersection is also equal to half that area of the missing square. So the top picture lacks half the area of the missing square from the perceived shape. The bottom picture protrudes half the area of the missing square from the perceived shape. Therefore, the sum of these two areas different from the perceived shape equals the displaced square in the bottom picture. For those who prefer math and numbers, here it is:
   Slope of blue square: 2/5
   Slope of red square: 3/8
   Perceived Profile Slope: 5/13 (line from A to B)
   Dimensions of “missing” triangle from the top picture :
   -Length Side 1 :sqrt(194) = 13.92838828
   -Length Side 2 :sqrt(73) = 8.544003745
   -Length Side 3 :sqrt(29) = 5.385164807
   -Area: 0.5 ( Combine this area to . . . . )
   Dimensions of “overlapped” triangle from the bottom picture :
   -Length Side 1 :sqrt(194) = 13.92838828
   -Length Side 2 :sqrt(29) = 5.385164807
   -Length Side 3 :sqrt(73) = 8.544003745
   -Area: 0.5 ( . . . . this are, and you get the missing square!)

   Reply
4. Sandeep September 5, 2008 at 1:04 pm

   @Ken: maybe you didn’t notice the link to the solution at the bottom, but very nice and detailed explanation

   Reply

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