Summary
Introduction
Is it a circle? Is it a square? Or is it both? Make your own 3D printed "ambiguous cylinder" illusion in this fun activity.
Materials
- 3D printed ambiguous cylinder shape. You can order the shape directly from sites like Shapeways or download a file to print yourself from sites like Thingiverse.
- Mirror
Instructions
- Order or print the ambiguous cylinder shape (see materials section).
- Place the cylinder on a table.
- Look at the cylinder from above at roughly a 45-degree angle.
- Rotate the cylinder slowly until you see either a circle or a square.
- Rotate the cylinder 180 degrees.
What shape do you see now? - Put the cylinder in front of a mirror.
What shape do you see in front of you? What shape do you see in the mirror?
- Pick the cylinder up. Look at it from directly above, then from the side. Try rotating it while viewing it from the top or the side.
What is the actual cross-sectional shape of the cylinder?
What Happened?
This cylinder seems impossible! When viewed from one side, it looks square. When viewed from the other side, it looks circular. When you put it in front of a mirror, you see both sides at once—so you will see a circle in front of you but the reflection of a square in the mirror, or vice versa. This illusion only works, however, when the cylinder is viewed from a certain angle. When you view it from the top, you will notice that it is neither a circle nor a square—it is in between the two.
Digging Deeper
If this cylinder's shapeshifting seems physically impossible, you are right. It is an optical illusion. The cylinder is carefully designed to look like a square from one side and a circle from the other side—but only when viewed from above at about a 45-degree angle. If you look at the cylinder from directly above, you will see its true shape.
You will also notice that the top and bottom surfaces of the cylinder are curved, not flat. Two sides curve upward, and two sides curve downward. When you view the shape from an angle, though, your brain tends to misinterpret the top surface as flat and adjust its perception accordingly. Your brain is tricked into thinking it sees a square or a circle, depending on which side you view the cylinder from.
See the publication by Professor Kokichi Sugihara in the Related Resources section for more examples of seemingly impossible shapes!
Ask an Expert
For Further Exploration
- Try the illusion on other people. Can they figure out how it works?
- What factors affect the illusion? For example, what range of viewing angles works for the illusion? Do lighting conditions (e.g., soft lighting versus harsh shadows) have any effect?
- Search for "ambiguous cylinder" on sites like Shapeways or Thingiverse. There are many other shapes you can try, including some that are more complex.
