Things You Never Knew...

2 Comments:

1. Anonymous said...
   9/12/2006 11:25 AM  
   The Big Triangle is the opitical illusion. The wrong assumption is that the hypothenuse of the big triangle is made up of that of the 2 smaller ones.
   
   This is based on an assumption that if you draw an actual hypothenuse, it converges exactly at the tip of the square where the 2 triangles meet. If not, you cannot use the grid to calculate area.
   
   For Proof:
   If the large Hypothenuse is a real hypothenuse, then all the angles of the 2 smaller triangles should be the same or the ratio of the length of the perpendicular sides should be equal.
   Smallest triangle: 2/5 = 0.4
   Larger triangle: 3/8 = 0.375
   Largest triangle: 5/13 = 0.385
   
   So the trick is that the angle of the largest triangle is in between that of the 2 smaller ones. Thus making the illusion feasible.
   
   More proof: the sum of all the parts is 32units2. the area of what we assume to be a triangle is 32.5units2.
   
   So in the first diagram, the point where the 2 trianlges meet is not the hypothenuse of the big triangle. In fact, the real hypothenuse of the big triangle should be at a point a little futher on the left.
   In the 2nd one, the same, just that the point of convergence is further to the left then where the hypotenuse of the big triangle should be, thus creating the extra space inside.
   
   So thats lunch anywhere i want?
   - Alex Toh
   
   http://a-mug-a-day.blogspot.com/2006/09/lingweis-puzzle-solution.html
   Anonymous said...
   9/14/2006 1:34 AM  
   damn it.. i knew the answer too.. oh well..
   
   -Clarissa

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