What is Pi: Symbol, Examples, and Values

Pi (π) in Maths

PI is one of the most interesting numbers used in mathematics. It is used as a constant in geometry, trigonometry, and many advanced branches of science. 

Students might have seen it while working with circles or measuring angles. But many students still ask: What is pi? To answer this question, we will explore the role of this constant in mathematics with clear examples to help students gain more insights into this unique number.

Read More: Parallelogram: Definition, Formulas, and Examples

What is Pi (π)Value?

Understanding what is PI value is essential in mathematics, especially in geometry and trigonometry. Many students often ask, "what is the value of π?" Pi, denoted by the Greek letter π, represents the ratio of a circle's circumference to its diameter.

Pi is the constant that represents the ratio of the circumference of a circle and the diameter of the circle. Therefore, the formula for pi is expressed as:

Pi = Circumference of a circle/Diameter of the circle

This ratio is always constant, irrespective of the size of the circle. For a circle of any size, dividing the circumference by the diameter will always give the same value, equal to pi. So, pi is a universal constant in mathematics. 

Pi Symbol

The symbol of pi is the Greek letter π, which was first introduced by the mathematician William Jones in 1706 and later popularized by the great mathematician Leonhard Euler.

The name of π came from the Greek word "perimetros," meaning "perimeter." It makes sense because the concept of pi relates to the perimeter or circumference of a circle.

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Value of Pi

It is an irrational number, meaning its digits of PI continue infinitely without repeating. While many approximate it as 3.14159, the full value of PI cannot be completely written due to its infinite nature. To summarize, PI is equal to 3.14159 in common calculations, but mathematically, it extends endlessly. The decimal value of pi contains an indefinite number of digits after 3. For practical calculations, we typically use the following values of pi:

• π ≈ 3.14 (as a decimal approximation)

• π ≈ 22/7 (as a fraction approximation).

Value of Pi in Decimals

When we talk about the value of pi in decimals, the approximated values we use are as follows:

• π ≈ 3.14 (rounded to two decimal places)

• π ≈ 3.1416 (rounded to four decimal places)

• π ≈ 3.14159265359 (up to 11 decimal places)

It is an irrational number, so the decimal value of π doesn’t give an exact value and continues indefinitely.

Pi (π) Formula 

When performing high-level math or computer simulations, knowing more digits of PI is useful, though for most purposes, the standard approximation suffices. Ultimately, PI is equal to the ratio of circumference to diameter, making what is the value of π a foundational question in understanding circles, spheres, and many mathematical formulas. There are various formulas used in mathematics, especially in geometry and trigonometry, that use pi. Some important formulas for pi (π) are mentioned below:

Circumference of a Circle

The circumference of a circle is expressed as

C = 2πr

where r = radius of the circle.

Area of a Circle

The area of a circle is expressed by the formula:

A = πr²

where r = radius of the circle.

Volume of a Cylinder

The volume of a cylinder is expressed by the formula:

V = πr²h

where r = radius of the cylinder and h = height of the cylinder.

Surface Area of a Sphere

The surface area of a sphere is calculated by the following formula:

A = 4πr²

where r = radius of the sphere

Volume of a Sphere

The formula for the volume of a sphere is:

V = (4/3) πr³

where r = radius of the sphere

These formulas show how pi is connected to circles, spheres, and other round shapes.

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Pi (π) Examples

Let’s apply the value of Pi in some examples.

1.  Find the circumference of a circle with a radius of 14 cm.

Solution:

Circumference of the circle = 2πr = 2x (22/7) x 14 = 2 x 22 x 2 = 88 cm

2. Find the area of a circle with a diameter of 10 cm.

Solution:

The radius of the circle = 10/2 = 5 cm.

The area of circle = πr² = 3.14 x (5) ² = 3.14 x 25 = 78.5 sq. cm.

3. Find the volume of a sphere with radius 3 cm.

Solution:

Volume of sphere = (4/3) πr³ = (4/3) x 3.14 x (3) ³ = 4 x 3.14 x 9 = 113 cm³ (approx.)

These examples show how π helps us calculate properties of circular and spherical objects.

Value of Pi in Degrees

One interesting use of π is in the measurement of angles. In mathematics, angles can be expressed in degrees or radians, and π connects these two systems.

We know that one complete revolution around the circle means rotation by 360°.

Again, by rotating 360° along the border of the circle, we get the circumference of the circle, which is equal to 2πr.

Therefore, we can say 2πr = 360°.

Or, πr = 180°

For a circle, 180° means an arc length of half the circle.

We know, radians = arc length/radius

So, for half of a circle, πr/r radians = 180°.

Or, π radians = 180

So, the value of pi in degrees is 180°.

Therefore, we can say:

• 90° = π/2 radians.

• 45° = π/4 radians.

• 60° = π/3 radians.

In this way, your child can make easy conversions between degrees and radians.

Also read: Binary to Octal Conversion - Definition, Methods and Examples

How To Calculate the Value of Pi?

Students can calculate the value of pi through an interesting activity. It involves the steps as mentioned below:

Step 1: Draw a circle of a certain radius.

Step 2: Take a thread and place it along the border of the circle so that it equals the perimeter of the circle.

Step 3: Place the thread along a ruler and measure its length.

Step 4: Calculate the value by dividing the circumference (length of thread) by the diameter (2 x radius) of the circle.

Step 5: The result is the value of pi.

Applications of Pi (π)

The concept of Pi is not only relevant in academics; it has applications in many other fields, as mentioned below:

• Architecture and Construction: For designing arches, domes, and circular structures, pi is used for calculation purposes.

• Astronomy: For calculating orbits of planets and stars, the value of pi is used.

• Engineering: Designing of wheels, gears, and circular components requires pi for calculations.

• Technology: The value of pi is used in signal processing, probability, and algorithms.

• Everyday Life: The formula involving pi is used for measuring areas and circumferences of circular objects.

In mathematical terms, pi (π) is the ratio of a circle’s circumference to its diameter, and it is approximately equal to 3.14159. The symbol of pi (π) has become one of the most widely used mathematical symbols in numerous applications. Pi is more than just a number; it’s a constant that connects geometry, trigonometry, and real-world applications.

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