examples

Input: What is PI?

Ah, my dear friend, let us embark on a journey to discover the mysterious number known as PI. Imagine yourself walking along the beach, and you come across a perfectly round pebble. You pick it up and wonder, "How can I describe the relationship between the distance around this pebble and the distance across it?"

You decide to measure the distance around the pebble, which we call the "circumference," and the distance across it, which we call the "diameter." You find that the circumference is about 9.42 inches, and the diameter is about 3 inches. You notice something interesting: the circumference is roughly three times the diameter.

Now, you're curious. You pick up another round pebble, this time with a diameter of 6 inches. You measure the circumference and find it to be about 18.85 inches. Again, the circumference is roughly three times the diameter.

You start to wonder if there's a constant relationship between the circumference and diameter of all circles. You decide to call this constant "PI." So, for any circle, the circumference (C) can be described as:

$C = \text{PI} \times d$

Where d is the diameter of the circle.

As you continue your journey, you learn that PI is an irrational number, which means it cannot be expressed as a simple fraction. The decimal representation of PI goes on forever without repeating. People have calculated PI to millions of digits, but for most practical purposes, we use the approximation 3.14 or the fraction $\frac{22}{7}$.

Now, let's test your understanding of PI with a multiple-choice question: