The research on "what is pi" dates back to 2000 BC.

Pi (pronounced as "pie") is a mathematical constant. It is an irrational number.

It is defined as the ratio of the circumference of the circle to its diameter.

The pi symbol is \(\pi\). It is also called Archimedes' constant.

The Greek mathematician, Archimedes, created an algorithm to approximate the pi value.

The simulation below shows the circumference of a circle whose diameter is \(1 \: \text{cm}\).

We all know that pi value is constant. It is an irrational number, and is usually, approximated to \(3.14\)

Let us now do a small activity to know what is pi exactly.

Draw a circle of any radius.

Use a thread and measure the diameter.

Now, bend this thread to form a curve and place it along the circumference of the circle.

You can also see this in the simulation below. Click on start animation to know how to do the activity

We observe that the diameter spans across the circumference three times and a little part of the circumference is left uncovered by our thread which is approximately \(0.14 \:\text{units}\).

Repeat this experiment with different diameters in the figure above and observe that there is always a shortfall of approximately \(0.14 \: \text{units}\) irrespective of the size of the circle.

This indicates that the circumference is approximately \(3.14\) times the length of the diameter.

The number \(3.14\) is the mathematical constant called the pi value.  

Let us understand where and what is pi used for? Pi is used to calculate the area and circumference of circles.

Any circular shape is dependent on the pi value. \(\pi\) is found in many formulae in trigonometry to examine the relationship between the lengths and angles of triangles and in geometry where we study about shapes, sizes, relative positions, and the properties of space. 

It is also used extensively in the field of architecture and robotics. pi\((\pi\)) is considered very important and hence, March 14 is celebrated as Pi day.

March 14 was the chosen day because March is the 3^rd month and we can denote the date as 3-14 which resembles the pi value.

Let us do a small activity to see how to calculate pi.

By the end of this activity, we will know what is pi exactly.

Draw a circle of diameter \(1 \:\text{cm}\).

Now take a thread and place it along the border of the circle (the circumference).

Now place the thread on the ruler and note the length.  

Repeat the process with diameters of \(2 \:\text{cm}\), \(3 \:\text{cm}\), \(4 \:\text{cm}\) and  \(5 \:\text{cm}\).

Record your observations in the table.

Diameter	Circumference	\(\begin{align}\frac{\text{Circumference}}{\textbf{Diameter}}\end{align}\)
\(1 \: \text{cm}\)	\(3.1\: \text{cm}\)	\[\frac{3.1}{1} = 3.1\]
\(2\: \text{cm}\)	\(6.2\: \text{cm}\)	\[\frac{6.2}{2} = 3.1\]
\(3\: \text{cm}\)	\(9.3\: \text{cm}\)	\[\frac{9.3}{3} = 3.1\]
\(4\: \text{cm}\)	\(12.4\: \text{cm}\)	\[\frac{12.4}{4} = 3.1\]
\(5\: \text{cm}\)	\(15.5\: \text{cm}\)	\[\frac{15.5}{5} = 3.1\]

We can observe that the ratio of circumference to diameter is always the same. This answers our question what is pi (\(\pi \)).

Now that we have understood what is pi and we've observed that the pi value is constant, let us see how to calculate it.

Pi is the ratio of the circumference of a circle to its diameter. The formula for calculating \(\pi \) is:

\(\begin{align} \pi = \frac{\text{Circumference}}{\text{Diameter}} \end{align}\)

Remember this line to recall the value of pi.

\( \pi = 3.141592.... \)

Value of Pi in Decimal

 

The value of pi is an irrational number.

It is non-terminating and non-recurring. 

Pi value approximate to \(10\) decimal place is \(3.141592653\)

For ease of calculations, it is often approximated to \(3.14\)

Value of Pi in Fraction

In the fractional form, the closest number to pi is \(\begin{align}\frac{22}{7} \end{align}\)

 

\(\begin{align}\frac{22}{7}\end{align}\) is a rational number.

On dividing \(\begin{align}\frac{22}{7},\end{align}\) we get the quotient which is a recurring decimal number but is close to the value of pi.

 

But, \(\begin{align}\frac{355}{133}\end{align}\) is more close to \(\pi\) than \(\begin{align} \frac{22}{7}.\end{align}\)

Divide and compare it with pi value.