Mathematical Applications - Pi

Application of Pi:

     Pi is one of the most extremely useful and fundamental quantities we know of. It is defined as the ratio of a circle's circumference to its diameter (or it area to the square of its radius).

It can obviously be used to calculate:

- the circumference of a circle (2 X π X r)
- the area of a circle (π X r X r)

Let's look at some more interesting facts about pi.

Ø  It is an irrational number, which means that its value cannot be expressed exactly as a fraction, when the numerator and denominator are integers.

Ø  It has an infinite number of non-repeating digits.

Ø  It is a transcendental number. This means that no sequence of algebraic operations using integers such powers, roots or sums can be equal to its value.

     Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.

Everyday Use:

     Pi appears in all sorts of calculations for physics, engineering, electrical systems. The double-helix is DNA revolves around pi. Pi is in the rainbow, the pupil of the eye, and when a raindrop falls into water pi emerges in the spreading rings. It appears in colors and in music. It is also used in probability and statistics.

     It also appears when calculating the number of deaths in a population. Interestingly, the ratio between the actual length of a river and its straight-line from source to mouth length tends to approach pi, Einstein being the one to show this. The current record for the decimal expansion of π, if verified, stands at 5 trillion digits.

     Thus, pi can be applied by many different types of people. Pi can turn out to be actually applied in many daily applications that many of us never even knew! To summarize some everyday uses, here are some of those uses:

1.      Electrical engineers used pi to solve problems for electrical application.

2.      Statisticians use pi to track population dynamics.

3.      Medicine benefits from pi when studying the structure of the eye.

4.      Biochemists see pi when trying to understand the structure/function of DNA.

5.      Physicists looking into the behavior of fluid ripples see pi and use it in their calculations.

6.      Clock designers use pi when designing pendulums for clocks.

7.      Aircraft designers use pi to calculate areas of the skin of aircrafts.

8.      Signal processing and spectrum analysis uses pi to find out what frequencies are in the wave that are used since the fundamental period of a sine wave is 2 X π.

9.      Pi can also be used for navigation, such as global positioning systems (GPS).

     Pi is commonly used for solving geometry, signalling, making probabilities and pi is also used for navigation.

     Let’s go into more details about pi being used for navigation. When planes fly great distances they are actually flying on an arc of a circle. The path must be calculated as such in order to accurately gauge fuel use. Additionally, when locating yourself on the globe, pi comes into the calculation in most methods.

     Pi can also be used in signalling during communication lines as well. Sine waves have a fundamental period of 2 X π, so pi becomes vital in signal processing, spectrum analysis such as when finding out what frequencies are in a wave that you have received or sent.