This equation represents the formula for the circumference of a circle:

$C = 2\pi r$

Explanation:

• $C$: Represents the circumference of the circle, the distance around the circle.
• $r$: The radius of the circle, which is the distance from the center to any point on the circle.
• $\pi$: A mathematical constant approximately equal to 3.14159.

This formula shows that the circumference is directly proportional to the radius, with $2\pi$ being the constant of proportionality.

Would you like a deeper explanation, practical examples, or further questions answered? Here are some extensions you might consider:

1. How is this formula derived from the definition of a circle?
2. What is the relationship between the circumference and the diameter ($d$)?
3. Can we calculate the radius if only the circumference is given?
4. How is $\pi$ determined or approximated in mathematics?
5. How does this formula apply in real-world problems, such as measuring distances or designing circular objects?

Tip:

Always remember that $\pi$ is a constant and does not change, which makes it fundamental in all circular geometry problems.