Photo source: PIN KORO

Geometry is the art of correct reasoning from incorrectly drawn figures. ~Henri Poincaré

Geometrical illusions are optical illusions where the mind perceives shapes, lines, or spatial arrangements in ways that differ from reality. These illusions rely on how we interpret geometric elements like angles, distances, and proportions. Our brain processes these shapes and their relations in ways that lead to misperceptions, creating visually striking and perplexing effects.

Geometry in optical illusions

Geometrical illusions exploit the brain’s natural tendencies to perceive shapes and dimensions in specific ways:

Vertical vs horizontal dimensions

Vertical lines often appear longer than horizontal ones. A rectangle of 8 cm high and 8.5 cm wide will be perceived as a square. And an ellipse that is 12 cm high and 11 wide will be perceived as a circle. That is, until you rotate the image 90 degrees. When it is wider than it is high, we can see it is an ellipse. And a person laying on the ground looks taller than a person standing.

This is caused by the way we perceive dimensions. We are more used to seeing objects in a horizontal orientation. As a result, our brain tends to overestimate vertical dimensions compared to horizontal ones.

Lines appear to be bent

When a straight line is drawn near a circle, so that it almost touches the circle, the line often looks slightly bent or curved near the circle. It appears to be “pulled” toward the circle, as if the circle is attracting it.

Divided sections

When you divide a surface in vertical sections (for example a piece of paper into 3 columns), the outer sections will always appear smaller than the central section, even though they are the same size.

This visual misjudgment happens in many places, such as in the facades of buildings or colonnades. The outer parts of a surface, next to the “air” or the background, seem smaller than the inner parts. Good artists and architects have taken this into account since ancient times.

Geometrical Illusions

Here are images from our collection of optical illusions with geometry.

Click on the images to see the larger version and read the explanation of the optical illusion and the source/credit of the image.