This is my response to the triangles presented at

Optical Illusions.

[img align=left]http://i73.photobucket.com/albums/i201/Arjuna77/Tri.jpg[/img]

The claim made is that “The coloured parts are exactly the same.” That is a false statement. Common sense says that it cannot be true. Proving it requires some work.

Both objects appear to be right triangles, but they are not. If you take a straightedge and place it on what appears to be the hypotenuse of the top image, you will find that it curves inward; since the line is not straight, the image is not a triangle. Likewise, what appears to be the hypotenuse of the bottom triangle curves outward. The illusion is made possible by this discrepency. The red and green portions of the top image are actually smaller than the corresponding portions of the bottom image. The bottom image covers a greater area than the top image. The difference in the areas is exactly the area of the added white square in the bottom image.

If you do not believe that what appear to be hypotenuses are actually curved by using a straightedge, you can prove it mathematically. The area of a right triangle is ½ times the base times the height. Assume both images are triangles. The total area is ½ times 13 times 5 = 32.5. The area of the red is ½ times 8 times 3 = 12. The area of the green is ½ times 5 times 2 = 5. The area of the orange is 7, and the area of the blue is 8. The botom figure has an additional white square with an area of 1. If you add up these areas to get the total area, you find that the area of the top figure is 32, and the area of the bottom figure is 33. Of course, both these measures contradict the fact that if these are right triangles the areas of both of them should be 32.5.

Another way of proving these images are not triangles is using the fact that the legs of similar right triangles are proportional. The base divided by the height of the whole image is 13 / 5 = 2.6. Assuming that we are looking at triangles, then the red and green images are similar to the total image. Their legs should be proportional to the legs of the total image, but they are not. For the red image, you get 8 / 3 = 2.6666, and for the green image you get 5 / 2 = 2.5. These discrepencies are slight, and the method used to adjust for them in this illusion is to curve the hypotenuse slightly inward in the top image and slightly outward in the bottom image.

If you told people that “Both images are squares”, they would know right away that they are being lied to. However, if you tell them that “The coloured parts are exactly the same”, almost everyone will accept it as the truth, even though saying that is as much a lie as saying that the images are squares.

The connection between this example and conspiracy theory is that many of the lies disseminated by corrupt leaders are carefully crafted and surrounded by enough truth so that most people do not notice the lie. Developing discernment is necessary to reveal these types of lies.