Welcome! Today we'll explore what pi is and why its value is approximately three point one four. Pi is one of the most important constants in mathematics. It represents the ratio of any circle's circumference to its diameter. No matter how big or small the circle is, this ratio is always the same number.
Now let's demonstrate this amazing property with circles of different sizes. Whether we have a small circle, a medium circle, or a large circle, when we divide the circumference by the diameter, we always get the same result: approximately three point one four. This consistency is what makes pi such a fundamental constant in mathematics.
Now, why do we say pi is approximately three point one four? The key word here is approximately. Pi is what mathematicians call an irrational number. This means its decimal representation continues forever without any repeating pattern. We can calculate pi to millions or even billions of decimal places, but we can never write down its exact value completely.
Let's work through a concrete example to see how we get three point one four. Imagine we have a circle with a diameter of exactly 2 units. When we measure around this circle, we find the circumference is approximately six point two eight units. Now we can apply our formula: pi equals circumference divided by diameter, which gives us six point two eight divided by 2, equals three point one four.
To summarize what we've learned: Pi is the fundamental ratio between a circle's circumference and its diameter. No matter what size circle we measure, this ratio is always approximately three point one four one five nine. Since pi is an irrational number, three point one four is simply a practical approximation that gives us sufficient accuracy for most everyday calculations.