Explanation
The symbol \(\pi\) (pi) is one of the most important numbers in mathematics.
Pi is the ratio between the circumference of a circle and its diameter.
In every circle:
\(\pi = \frac{C}{D}\)
where:
- \(C\) is the circumference (distance around the circle)
- \(D\) is the diameter
No matter how large or small the circle is, the value of:
\(\frac{C}{D}\)
is always approximately:
\(\pi \approx 3.14\)
This means the circumference is a little more than 3 times the diameter.
For example:
- if the diameter is \(1\) meter,
- then the circumference is about \(3.14\) meters.
\(\pi\) helps us calculate:
- circumference
- area of circles
- arcs
- curved distances
and many other important ideas in mathematics, physics, and engineering.
Formula / Rule
Definition of \(\pi\)
\(\pi =\frac{C}{D}\)
Circumference Formula
\(C= \pi D\)
or equivalently:
\(C=2\pi r\)
where:
- \(C\) = circumference
- \(D\) = diameter
- \(r\) = radius
Example
Suppose a circle has diameter:
\(D=100 m\)
Using:
\(C=\pi D\)
and approximating:
\(\pi \approx 3\)
we get:
\(C \approx 3×100 = 300 m\)
So, the circumference of the circle is approximately:
\(300 m\)
Now imagine walking only along the upper half of the circle.
The semicircle distance is:
\(\frac{1}{2} C\)
So:
\( \frac{1}{2} (300) = 150 m\)
This means:
- walking directly across the diameter takes about \(100 m\)
- walking along the upper curved path takes about \(150 m\)
So the curved path is about half more than the direct distance.