# How is the number Pi, derived?

• ruko
In summary, Pi (π) is derived by finding the ratio of a circle's circumference to its diameter. It has been calculated to many decimal places through methods such as infinite series and circumscribed polygons. Its calculation has a long history dating back to the ancient Greek mathematician, Archimedes, and continues to be used in modern calculations.
ruko
How is the number 3.14159...etc, derived? I know it has been calculated out to very great lengths and I'm wondering how it's done.

Just find the proportion of radius to circumferance, I believe. I know it is some kind of proportion.

My personal favourite:

$$\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots\!$$

Modern calculation of pi no doubt use infinite series, first formulated in Newton's time (mid 1600's). Archimedes used circumscribed polygons w/ 96 sides to calculate pi with three digit accuracy.

## 1. What is the value of Pi?

The value of Pi is approximately 3.141592653589793. It is an irrational number, which means it cannot be expressed as a finite decimal or a fraction. It has an infinite number of digits after the decimal point.

## 2. How is Pi calculated?

Pi is calculated by dividing the circumference of a circle by its diameter. This ratio is constant for all circles, regardless of their size. It has been calculated to over one trillion digits, and the quest for more digits continues.

## 3. Who discovered Pi?

The concept of Pi has been known for thousands of years, with ancient civilizations such as the Egyptians and Babylonians using approximations of Pi in their calculations. The Greek mathematician Archimedes is credited with the first rigorous calculation of Pi in the 3rd century BC.

## 4. Can Pi be represented in a simple fraction?

No, Pi cannot be expressed as a simple fraction. However, it can be approximated by using fractions such as 22/7 or 355/113, but these are still not exact representations of Pi.

## 5. What are the practical applications of Pi?

Pi is used in various fields, including mathematics, physics, engineering, and even art. It is essential for calculations involving circles, such as finding the area, circumference, and volume of a circle. It is also used in navigation and GPS systems, and in the development of computer algorithms.

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