# ​ QUestion: {Please don't provide any web link or certified answer for the below question. Please provide only experts answer. Answer the following with the help of diagram and examples.  Explain the optical illusion in Maths for making a working model on it.​

Hi,
Optical illusions are pictures that play tricks on our eyes and baffle our perception. They are not the result of faulty vision. Depending on light, viewing angle, or the way the picture is drawn, we may see things that aren't there – and often don't see what's right under our nose. These tricks of the eye and mind have been part of human experience since the beginning of history. The ancient Greeks made use of optical illusions to perfect the appearance of their great temples. In the Middle Ages, misplaced perspective was occasionally incorporated into paintings for practical reasons. In more recent times, many more illusions have been created and implemented in the graphic arts.

In mathematics optical illusion covers  3- Dimentional part where images appears to be in three dimension although drawn in 2- dimentional paper sheet.
For example;-
A cube and a prism

Now here we can see that it appears they are occupying the space , or having volume , or in easy words appears to be in three dimension.

Donald D. Hoffman ​uses mathematical concepts to try to explain how our brains construct the images we see. He calls them rules. Rule 1. Always interpret a straight line in an image as a straight line in three dimensions.

Rule 2. If the tips of two lines coincide in an image, then always interpret them as coinciding in three dimensions.

So, for example in the image on the left, the diagonal lines intersect in the image and hence your brain uses rule 2 to construct a three dimensional image where these lines intersect, forcing it to be flat.

The "optical illusion" where this can be seen is the devil's triangle or impossible triangle.

Rules 1 and 2 force you brain to try to construct a three dimensional object where lines in the image are lines in three dimensions, and coinciding lines in the image are coinciding lines in three space. However a different image shows that your brain might be using the rules to construct the wrong object.

This is two sticks lying an a table and the third stick, on the right, standing vertically. Now move your head to the right until the top end of the vertical stick coincides with the far end of the stick on the table. What you see is the impossible triangle.

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