Magic Arcs

An optical illusion where identical arcs the stretch and shrink.

It’s probably the world’s most baffling optical illusion. Hold one arc above the other and ask the question, “Which arc is bigger?” The bottom arc will always look bigger than the top one, yet they are actually the same size! Reverse the arcs to make the other one look bigger. What you see is not always what you get! Keep reading and we’ll let you in on some presentation ideas and stunts that will really amaze and fool your friends.

Experiment Materials

  • 2 identical coffee sleeves
  • Adult supervision


  1. Obtain two identical coffee sleeves from your favorite coffee house or by removing them from used coffee cups.
  2. Unfold and flatten each of the sleeves.
  3. Hold one sleeve above the other with the sleeves arcing in the same direction. Hold the arcs so that one end is lined up. Whoa… the top arc is smaller! “Stretch” the top arc and switch the arc positions. Now the same arc is bigger!
  4. Place the arcs on top of each other to show they are the same size.

How Does It Work?

This is an illusion of comparison. Psychology textbooks tell us that a segment of a circle seems much longer if it is placed under an identical segment in such a way that the ends are even at one end. The secret is that the longer outside edge of the bottom arc is being compared against the shorter inside edge of the top arc. When the inside curve of the top arc is placed next to the outside curve of the bottom arc, the bottom arc always appears to be bigger.