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What is Pi

What is Pi

William L. Schaaf, A famous professor of mathematical education, says that “Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception, and human interest as the number pi.”  Do you know what is pi? Pi is a mathematical constant and the ratio of the circumference of a circle to its diameter.

In this blog, you will learn what pi is, how it originated, and how it is used in mathematics. 

Explanation of Pi 

Pi, represented by the Greek letter π, is the ratio of the circumference of a circle to its diameter. It is a mathematical constant with the value equal to 3.14159. Regardless of the size of the circle, the ratio of its circumference and diameter is always equal to pi (π). 

The concept of this constant has been used by early mathematicians. However, the symbol was first used by William Jones in 1706. 

Let’s explain the pie with the help of the diameter and circumference of the circle. 

Look at the circle shown below. 

The distance that covers the outer edge of a circle is the circumference. As shown in black. The thickness of a circle is its diameter, shown in red. 

If we wrap the diameter around the circumference of the circle, it will take three and some portion (.1415) to complete it. The circumference of a circle is approximately 3.14 times its diameter. So, 3.14159 diameter equals a circumference. It is constant for all circles, regardless of their size. This constant is known as pi. It is represented as;

π=circumferencediameter\pi = \frac{\text{circumference}}{\text{diameter}}
π=circumferencediameter=3.14\pi = \frac{\text{circumference}}{\text{diameter}} = 3.14
Explanation of Pi

Pi in Fraction Form

Pi (π) is an irrational number and cannot be expressed as an exact fraction. Generally, pi in fraction form is written as 22 over 7, i.e,  227. It is not the exact value, but used for approximation. Another fraction that is used to express

πis355113\pi is \frac{355}{113}

It provides a more accurate approximation of pi. 

Applications of Pi

Pi has several applications in science, math, physics, and other subjects. It has important usage in trigonometry and geometry involving angle measurement, circles, spheres, and other curved shapes.  

Calculating the circumference of a circle 

Pi is used to find the circumference of a circle. As per the definition, it is the ratio of the circumference and diameter of the circle, given as;

π=circumferencediameter\pi=\frac{circumference}{ diameter}

From this formula, we can find the circumference of a circle if the diameter is given. 

π=circumferencediameter\pi=\frac{circumference}{diameter}
Circumference=diameter(π)Circumference=diameter ( \pi)

As the diameter is equal to 2r, the formula to find the circumference will become;

Circumference=2πrCircumference=2\pi r

Example

Find the circumference of a circle if its diameter is 6 cm.

According to the given condition, if the diameter is 6 cm, then the radius of the circle will be 3 cm.

The circumference of a circle is given as;

Circumference=2πrCircumference=2\pi r
Circumference=2π(3)Circumference=2\pi(3)
Circumference=2π(3)Circumference=2\pi(3)
Circumference=2(3.14)(3)Circumference=2(3.14)(3)
Circumference=18.84cmCircumference=18.84cm

Area of circle

The area of a circle can be found if the radius of the circle is known. The area is given as 

A=πr2A = \pi r^2

Example 

Find the area of a circle if the radius of that circle is 2 cm.

To find the area of a circle, we will use the formula.

A=πr2A = \pi r^2
A=3.14(2)2A = 3.14(2)^2
A=3.14(4)A = 3.14(4)
A=12.56cmA = 12.56 cm

Besides the circle, pi is also used in trigonometry. 

Radians

Pi is the base for defining radians, a unit of angular measurement. A full circle is 2π radians, meaning π radians is equivalent to 180 degrees. 

Trigonometric Functions Pi is used to define special angles within the trigonometric functions. For example,

sin⁡(π2)=1\sin\left(\frac{\pi}{2}\right) = 1
cos⁡(π)=−1\cos(\pi) = -1
sin⁡(π)=0\sin(\pi) = 0

Square Root of Pie

A number that gives a specified quantity when it is multiplied by itself is known as the square root. The square root of pie can be found with the help of the long division method. 

Let’s look at the long division method to find the square root of pi 3.14. The value of pi is 3.14, so it can be solved by method explained below. 

Square Root of Pie

So, the square root of Pi equals 1.772.

Conclusion 

Pi (π) is a mathematical constant that is equal to 3.14159. It represents the ratio of the circumference of a circle to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction.

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