Value of Pi: Definition, Fraction, Area of a circle, circumference of a circle and Diameter

Pi is defined as the ratio of the circumference of the circle to its diameter. The value of pi is approximately 3.1416. It is obtained if we divide the circumference of a circle (the total distance around the circle) with the diameter, and it stays the same irrespective of the circle size. The value 3.1416 is commonly considered as the universal value of pi. Most of the trigonometric problems and geometric problems use this pi value to arrive at the results. Pi is represented by the symbol π. This mathematical constant comes from a Greek alphabet.

The value pi can be considered an irrational constant as it has infinite values after the decimal point. It consists of never-ending values and, therefore, cannot be used as a common fraction. Often, 22/7 is widely used for calculating the pi value. It is proven that pi has no exact or accurate value due to its infinite decimals.

The circumference of a circle is the arc length of the circle surrounding its perimeter. Diameter is simply obtained by multiplying the radius of the circle (multiplied by 2). Likewise, in order to calculate the circle's area, the pi value is used. Area of the circle can be said as,

Area of a circle = pi * r * r

Where,

Pi = 3.14

R = radius

The value of pi, 3.14, is substituted to the above formula to obtain the area of a circle.

Area of a circle = A=πr²

For instance, an athlete runs around a circular ground track with a diameter of 200 m. In order to calculate the total distance covered if he finishes one complete revolution of the garden, we need to calculate the circumference of the ground.

The circumference of a circle = * diameter

= * 200 m

= 3.14 * 200

= 628 m

Hence, the athlete covers approximately 628 m when he does one complete round of the ground.

While calculating the value of pi, one should keep in mind the following prerequisites:

• The value of pi can be obtained only if the figure is an exact circle. It is impossible to calculate the pi value from ovals or arcs, or ellipses. A circle can only be formed when all points on the plane are placed equidistant from a single centre point.
• The exact measurement of a circle's circumference is a must to arrive at the Pi value. The circumference is the length of the circle around its edges.
• The diameter must be measured accurately to obtain the accurate Pi value. The diameter is twice that of the radius and is attained by measuring a circle from one side to the opposite side through the centre point.

Diameter of a circle = 2πr

• The formulae should be used precisely in order to obtain Pi.
• Pi is widely used to compute calculations concerning circles, spheres and cylinders.
• Other mathematical calculations such as the sum of infinite series also use Pi.

Apart from just mathematical applications, the usage of Pi finds its way in science, physics and medical fields as well.