The Bullseye illusion is a geometric optical illusion.

Contents

• Description
• Mathematical background
• External links
• References

Description

In Figures 1 to 4, the green circle appears larger than the blue ring. In reality, however, both areas have the same area.

• 
  Figure 1
• 
  Figure 2
• 
  Figure 3
• 
  Figure 4

Mathematical background

The blue ring is formed by the difference in area between a larger circle with radius c and a smaller circle with radius b.

Let the green circle have radius a. Then the condition for the equality of the two areas is:

${\displaystyle \pi a^{2}=\pi c^{2}-\pi b^{2}}$, i.e.,

${\displaystyle a={\sqrt {c^{2}-b^{2}}}}$.

For the special case ${\displaystyle a=b}$ (Figure 4), the condition for the equality of the two areas is:

${\displaystyle \pi b^{2}=\pi c^{2}-\pi b^{2}}$, i.e.,

${\displaystyle a=b={\frac {c}{\sqrt {2}}}}$.

In this case, the larger circle is completely decomposed into the smaller green circle and the blue ring of equal area. ^{[1] [2]}

External links

• Bullseye illusion Wolfram MathWorld
• Bullseye illusion (interactive demonstration) Wolfram Demonstrations Project
• Bullseye optical illusion from math-fail.com

References