Why is PI Everywhere? Exploring its Impact

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In summary, pi is a mathematical constant that is frequently found in various scientific studies, particularly those involving circles, spheres, and balls. It is similar to other constants like hbar, c, and k, which are necessary for working with different concepts in physics. While there may not be a specific book explaining the prevalence of pi, understanding its use in mathematics can help make connections to its appearance in various scientific theories.
  • #1
goldsax
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we all know the PI crops up everywhere..

why for example would PI be found in the equation for the density parameter of the cosmological constant etc..
is there a book that can explain why PI rears its head up in all types os studies...

cheers
 
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  • #2
Anything that involves any kind of cirlcle, sphere or ball is going to involve pi, it crops up in densities and the likes because it's convenient to work with densities of 'balls' (especially if they are rotationally symmetrical!).
It's just like hbar in quantum mechanics, c in relativity and boltzmans k in thermodynamics (assuming we're not working in specialised units where certain constants are set = 1)
No pi = not working with cirlces, spheres etc
No hbar = classical limit
No c = non relativistic limit
No k = working at absolute zero

edit;
In regards to books, none that I know of will explicitely point this out but once you get use to the theories you'll start to see links between these physical constants and where they come from.
 
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  • #3
@genericusrnme
Pi can also be the result of mathematics. Pretty much any function that involves sin/cos/tan ect is going to involve a Pi somewhere. This isn't surprising because how we define radians. It can also be found frequently when complex numbers come up (usually because of the relationship to geometric and exponential functions).
 
  • #4
Hologram0110 said:
@genericusrnme
Pi can also be the result of mathematics. Pretty much any function that involves sin/cos/tan ect is going to involve a Pi somewhere. This isn't surprising because how we define radians. It can also be found frequently when complex numbers come up (usually because of the relationship to geometric and exponential functions).

The trig functions and your e[itex]^{ix}[/itex] are still related to circles, namely the unit circle! o:)
 
  • #5
i will be doing maths as my next module..so will be further able to understand the concepts,
thanks for pointing the way...
 
  • #6
goldsax said:
i will be doing maths as my next module..so will be further able to understand the concepts,
thanks for pointing the way...

No problem buddy :biggrin:
 

1. Why is PI Everywhere?

PI, or the mathematical constant pi, is everywhere because it is a fundamental part of mathematics and has numerous applications in the fields of science, technology, and engineering. Its value, which is approximately 3.14, is used to calculate the circumference, area, and volume of circles and spheres, making it essential in fields such as geometry, trigonometry, and calculus. In addition, pi appears in many natural phenomena, such as the ratio of a circle's circumference to its diameter, and is also used in various equations and formulas in physics and engineering.

2. What is the impact of PI Everywhere?

The impact of PI Everywhere is significant and far-reaching. Its widespread use in mathematics and various scientific fields has led to advancements in technology and innovation. For example, pi is crucial in the design and construction of buildings, bridges, and other structures, as well as in the development of computer algorithms. It also plays a vital role in understanding and predicting natural phenomena, such as the motion of planets and the behavior of waves. Overall, the widespread presence of pi has greatly influenced the development of human knowledge and progress.

3. How does PI Everywhere affect our daily lives?

PI Everywhere has a direct impact on our daily lives, even if we may not always realize it. From the technology we use, such as smartphones and computers, to the buildings we live and work in, pi is present in various forms. It also plays a role in everyday activities, such as measuring and cooking, as well as in industries such as transportation and medicine. In short, the constant presence of pi affects many aspects of our daily routines and interactions with the world around us.

4. Why do we use PI in mathematics instead of a different number?

The value of pi has been used in mathematics for thousands of years, and it is deeply ingrained in the foundation of the subject. It is an irrational number, meaning it cannot be expressed as a simple fraction, making it useful for calculations involving circles and other curved shapes. Additionally, pi is a universal constant, meaning it has the same value regardless of the size of the circle, making it a reliable and consistent tool for solving mathematical problems. Other numbers, such as 3 or 4, do not have these same properties and are not as versatile as pi.

5. What are some interesting facts about PI Everywhere?

There are many interesting facts about PI Everywhere, including its value, which has been calculated to over one trillion digits. The first known use of pi dates back to ancient Egypt and Babylon, where it was estimated to be around 3.125. In 2019, a physicist used a supercomputer to calculate pi to a record-breaking 31.4 trillion digits. Pi also has its own day of celebration, March 14th (3/14), and has inspired numerous artistic and cultural works. Furthermore, pi has been the subject of much fascination and mystery, with many people attempting to find patterns or hidden messages in its digits.

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