What is Pi?

In this fun lesson, we will learn about what is pi (pronouced as pie), the pi symbol, the pi number, and the pi circle in the concept of what is pi. Check-out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. So, what are you waiting for? Let's have a slice of this pi.  

Did you know that the Ancient Greeks attempted to study pie in 2000 BC? Over millennia, these are the inferences that have been derived that include the fact that pi is an irrational number, it is teh ratio of the circumference of the circle to its diameter. 

The pi symbol is \(\pi.\) It is also called Archimedes' constant after the Greek mathematician, Archimedes, who created an algorithm to approximate the pi value. The simulation below shows the circumference of a circle whose diameter is \(1 \: \text{cm.}\)

Lesson Plan

What is Pi in Maths?

We all know that pi value is constant. It is an irrational number 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.


Formula for Pi

Now that we have understood what is pi, and we have 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 formula - approximate value of pi

pi number approximated to 6 decimal place is

 \( \pi = 3.141592 \)

How to Calculate Pi?

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 \(1 \:\text{in}\).

A circle of diameter 1 centimeter

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

A rope around the circle.

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

Rope length is 3.14 centimeter

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

Circumference measure of a circle of diameter 2 cm

Record your observations in the table.

Diameter Circumference \(  \dfrac{\textbf{Circumference}}{\textbf{Diameter}}\)
  \(1 \: \text{in}\)   \(3.1\: \text{in}\) \(\frac{3.1}{1} = 3.1\)
  \(2\: \text{in}\)   \(6.2\: \text{in}\) \(\frac{6.2}{2} = 3.1\)
  \(3\: \text{in}\)   \(9.3\: \text{in}\) \(\frac{9.3}{3} = 3.1\)
  \(4\: \text{in}\)   \(12.4\: \text{in}\) \(\frac{12.4}{4} = 3.1\)
  \(5\: \text{in}\)   \(15.5\: \text{in}\) \(\frac{15.5}{5} = 3.1\)

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


100 Decimal Places of Pi

Value of Pi in Decimal

 pi in mathematics - decimal  value

The value of pi is an irrational number.

Pi number is non-terminating and non-recurring.

Pi value approximated to \(100\) decimal places is

\[\begin{matrix}3.1415926535 &8979323846 &2643383279 \\ 5028841971 &6939937510 &5820974944 \\ 5923078164 &0628620899 &8628034825 \\ 3421170679 \end{matrix}\]

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

 
important notes to remember
Important Notes
  1. \(\ \pi\) is a mathematical constant which is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to \( 3.14159\)
  2. Basic circle formula with pi
    a)\(\text{ Circumference}\!=\!\pi\! \!\times\!\text{Diameter}\)
    b)\(\text{ Area}= \pi \text{r}^2\)

Solved Examples

Example 1

 

 

A pizza of diameter \(14 \: \text{in}\) is divided into \(6\) equal parts. What is the area of each slice?

A circular pizza of diameter 14 cm

Solution:

Radius of the pizza

\[\begin{align}&= \frac{\text{Diameter}}{2}\\
&= \frac{14}{2} \\
&= 7 \:\text{in}
\end{align}\]

Area of the pizza

\[\begin{align}
&= \pi\: r^2 \\
&= \frac{22}{7} \times 7 \times 7 \\
&= 154\: \text{in}^2
 \end{align}\]

Thus, total area of the pizza is \(154\: \text{cm}^2\)

Area of a slice of the pizza

\[\begin{align}
 &= \frac{\text{Area of the pizza}}{\text{Number of slices}}\\
&=\frac{154}{6} \\
&= 25.66 \:\text{in}^2
 \end{align}\]

\(\therefore \; \) Area of a slice of pizza \(= 25.66 \:\text{in}^2\)
Example 2

 

 

John had to replace a leaky pipe. He measured \(44 \:\text{mm}\) around the outside of the pipe. What is the diameter of the pipe he should buy?

A circular pipe of circumference 44 cm , apply the circle formula with pi to  find the diameter

Solution:

Circumference of the given pipe is \(44 \:\text{mm}\)

\[\begin{align}
&= 2 \pi\text{r}\\
44 &= 2 \times\pi \times \text{r} \\
44 &= 2 \times \frac{22}{7} \times {r} \\
\therefore \text{r} &= 7 \:\text{mm}
\end{align}\]

Therefore, diameter of the pipe

\[\begin{align}
&= 2  \times \text{r}\\
 &= 2 \times 7 \\
 &= 14 \:\text{mm}\\
 \text{D} &= 14 \:\text{mm}
\end{align}\]

\(\therefore\) Diameter of the pipe \(= 14 \text{ mm} \)
Example 3

 

 

Betty measured the diameter and circumference of a hula loop accurately.

The diameter was \(113 \:\text{in}\) and the circumference was \(355 \:\text{in}\)

She used these measurements and calculated \(\pi\). Is her value close to the real value of \(\pi\)?

A hoopla loop of diameter 113 cm and circumference 355 cm

Solution:

We know that \(\pi\)

\[\begin{align}
 &= \frac{\text{Circumference}}{\text{Diameter}}\\
&= \frac{355}{113} \\
&= 3.1415929
\end{align}\]

\(\therefore \; \)\(\begin{align} \frac{355}{113} \end{align}\) is very close to the pi value.
Example 4

 

 

Ria goes jogging in a park daily.

The park is shaped semicircular as shown. The diameter of the park is \(70\: \text{yd}\).

If she goes around the park \(10\) times. How much distance does she cover?

 Semi circular park of diameter 70 m

Solution:

Perimeter (circumference) of the circle 

\[\begin{align}
 &=    \pi \times \text{d} \\
&= \pi  \times 70 \\
&= 70 \pi
\end{align}\]

Perimeter (circumference) of the semi circle

\[\begin{align}
&= \frac{\text{circumference}}{2} + \text{diameter} \\
 &= \frac{70 \pi}{2} + 70  \\
&= 35 \pi +70  \\
&= 35  \times \frac{22}{7} + 70 \\
&= 110 +70\\
&= 180 \: \text{yd}
\end{align}\]

Ria goes around the park \(10\) times.

Therefore, the total distance covered by her

\[\begin{align}
&= 180 \times 10 \\
&= 1800 \text{ yd} \\
\end{align}\]

\(\therefore \; \)Ria covers a distance of 1800 yd.
 
tips and tricks
Tips and Tricks
  1. "How I Wish I Could Calculate Pi" - rembember this line to recall the value of pi (How - 3, I - 1, Wish - 4 , I - 1 Could - 5, Calculate - 9 Pi - 2) \(\pi = 3.141592\)
  2. Based on the problem, for ease of calculation, use \(\pi\) value as \(\frac{22}{7}\) or \( 3.141592\)

Interactive Questions

Here are a few problems related to pi

Select/type your answer and click the "Check Answer" button to see the result. 

 
 
 
 
 
 

Let's Summarize

We hope you enjoyed learning about What is pi ? with the simulations and practice questions. Now you will be able to easily solve problems on What is pi, pi symbol, pi number, pi circle.

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Frequently Asked Questions (FAQs)

1. What are the first 100 digits of Pi?

The first 100 digits of Pi are 

3.1415926535 8979323846 2643383279
5028841971 6939937510 5820974944
5923078164 0628620899 8628034825
3421170679    

2. What is Pi exactly?

Pi in mathematics is a constant which is the ratio of the circumference of a circle to its diameter. It is an irrational number often approximated to 3.14159

3. Will Pi ever end?

Pi value will never end. It is an irrational number. It is a non-terminating and non-recurring number.

4. Why is Pi important?

  • Pi in maths 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.
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