Optical illusions with geometry

Some optical illusions with geometry that will help students be on guard when they are looking at an image and not always believe things that they see. The concept of making our brain see things that do not exist and/or distorting an image so it will send the wrong information to the brain is called optical illusions.

Example #1:

Which line is bigger in the letter T?

The letter T above is made with a horizontal segment and a vertical segment. When we were kids, the teacher taught us to make the vertical line bigger. Therefore, in our mind, we always expect the vertical line to be bigger whenever someone shows the letter T.

Using the figure above, when you compare the length of the vertical segment to the length of the horizontal segment, what do you notice?

The vertical segment appears to be longer. However, both segments have the same length. When I made the letter T, I made sure that both lines have the same length. Again, the reason this one tricked you is because people usually expect that the vertical line in the letter T will be bigger.

Example #2

The image below shows another obvious example of optical illusion or trick that can challenge the best of us.

In the parallelogram above, segment AB appears to be longer than segment AC. In reality, when I created the image, I made sure that segment AB is the same length as segment AC. If you do not believe me, just get a ruler or a compass to verify that this is indeed the case!

Most likely what tricked you is the fact that segment AC was placed in a smaller parallelogram.

A couple more interesting optical illusions with geometry.

Example #3

In the image above, we see two segments. The one on top appears to be smaller than the one at the bottom. Again, these two segments have the same length. Can you tell why this one tricked you into thinking that the one at the bottom is bigger?

Example #4

Our last example shows again how dangerous it is to rely solely on our visual observation when drawing conclusions about a figure. A quick look reveals that the arc at the bottom is longer.

However, once again they both have the same length. What tricked you into thinking that the one on top is shorter?