π

The Magic of Pi (π)

Unlocking the circle's oldest secret

🤔 What is Pi?

Pi (π) is simply the ratio of a circle's circumference to its diameter. No matter how big or small the circle, if you divide its perimeter by its diameter, you always get exactly 3.14159...

π = Circumference (C) Diameter (d)

🔴 Understanding the Formulas

Because π = C / d, we can multiply both sides by d to get the formula for the circumference:

  • Circumference: C = πd   (or C = 2πr since d = 2r)
  • Area: A = πr²   (You'll prove this visually!)

💡 How to Use This Lab

  • Unroll Mode: Change the diameter, then drag the slider to physically "unroll" the circle's edge onto a ruler. See exactly where it lands!
  • Pizza Slices (Area): Cut the circle into pieces and rearrange them into a rectangle to prove A = πr².
  • Irrational Nature: Watch Pi calculate to countless decimal places. It never ends and never repeats!
Diameter (d)1.0
Perimeter (C)0.000
Ratio (C/d)--
Roll the Circle: