As a child i once arrived at the conclusion that the area of a given circle would be equal to that of a square with a distance around it equal to the circumference of the circle. So the area of a given circle with a circumference C, would be (C/4)^2.
I stubbernly tried to defend this principle during math class. A countering example was quickly found...
A childhood belief about counting

others believed things like this
- I used to believe that 7 times 12 was equal to 83 or 84, depending on the math problem.— Eric Swensen
- I used to believe that rounding a number meant drawing a circle around it.Anon
- Until I was about 8 I believed that your back teeth keep growing in until you have a full circle of teeth.Anon
- I used to think that "No standing signs" meant that you weren't allowed to actually stand in the area!Anon
- Well into adulthood I thought that a local anesthetic meant one from the area near the hospital..— D'sparil
- Huey Lewis's "Hip to be square" - in 3rd grade I could have SWORN it was "hit the beef square". ????Anon