# Value of Pi

## Value of Pi

The value of pi, symbolized by π, is the ratio of a circle's circumference to its diameter. This constant is also known as Archimedes' constant, named after the Greek mathematician Archimedes, who developed a method to approximate pi. Being an irrational number, pi has an infinite number of digits beyond the decimal point. Commonly represented as 3.1415929 or as the fraction 22/7, pi is fundamental in geometry for calculating the surface area, volume, and circumference of various three-dimensional shapes.

## What is the Value of Pi?

The value of 'pi' is constant and unchangeable. It is an irrational number, typically approximated as 3.14. Pi is widely used in various mathematical formulas for determining the surface area and volume of numerous solid shapes. Pi represents the ratio of a circle's circumference to its diameter. The diameter, the longest line segment passing through the center of the circle, can be visualized as wrapping around the circle's circumference. This process reveals that the circle's circumference is approximately 3.14 times its diameter.

If we divide the circumference of a circle by its diameter, we get a value close to 3.14. It is important to note that, regardless of the circle's size, the ratio of its circumference to its diameter remains constant.

## Formula for Pi

The value of pi can be determined by dividing a circle's circumference by its diameter. The formula for calculating π is:

π = Circumference/Diameter

### Pi is an irrational number

Pi is an irrational number, meaning it has an infinite number of decimal places without repeating patterns. The first 100 decimal places of pi include all digits from 0 to 9. Specifically, there are eight 0's, eight 1's, twelve 2's, eleven 3's, ten 4's, eight 5's, nine 6's, eight 7's, twelve 8's, and fourteen 9's. The image below illustrates that pi's decimal representation begins with 3 and does not terminate or repeat.

Pi's decimal expansion is non-terminating and non-recurring. For simplicity, pi is often approximated as 3.14.

### Value of Pi in Fraction

Because 180 degrees is equivalent to radians, the value of pi in degrees is 180. To understand this, we need to explore the concept of radians, which is the SI unit for measuring angles. The circumference of a circle represents one full revolution. This means that rotating 360 degrees around a central point at a fixed distance (radius) gives us the circumference, which equals *2πr*, where *r* is the radius of the circle. Hence, Circumference = *2πr = 360* degrees. For half a circle, the angle is 180 degrees, and the arc length is *πr / 2 = r*. Radians are calculated by the formula arc length/radius. Thus, for half a circle, the arc length is *πr* and the radius is *r*.

→ *πr/r* radians = 180°

→ *π* radians = 180°

Thus, the value of pi in degrees is 180 degrees.

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