I understand the mathematical definition of Pi, but why does it end up being used in so many formulas and applications in math, engineering, physics, etc? What does it unlock?
Edit: I understand Pi is the ratio of circumference to diameter. But why is that fact make it important and useful. For example it shows up in the equation for standard normal distribution. What does Pi have to do with a normal distribution. That’s just one example.
In: 3
Pi is what’s called a “mathematical constant”.
This means, it’s a number that appears in a surprisingly varied number of places. It’s a number that the *universe* has chosen as important, and not humanity. And given how interesting the number is, that only makes it all the more incredible that a precise a number as pi is can appear everywhere, even when you’re not looking for it.
It most commonly is used to represent the ratio of the circumference of a circle to its diameter. It is a non-repeating, non-terminating decimal (basically, it goes on seemingly infinitely) that has been calculated to over 31 trillion digits, making it one of the most well-known and fascinating mathematical constants.
As to why it’s important
1. It is a fundamental constant in mathematics: Pi appears in many mathematical formulas and equations in various fields of mathematics, such as geometry, trigonometry, calculus, and number theory. It is used to calculate the area, volume, and circumference of circles, spheres, and cylinders, among other shapes. Knowing Pi is key to understanding these things.
2. It has practical applications: Pi is used in many real-world applications, including engineering, physics, and astronomy. For example, it is used in calculations for designing bridges, buildings, and other structures, as well as in satellite and space navigation systems.
3. It has cultural significance: Pi has been studied and celebrated by many cultures throughout history. It has been represented in art, literature, music, and even in the design of buildings and monuments. Pi Day, which is celebrated on March 14th (3/14) every year, has become a popular celebration of math and science.
4. It is a challenging and fascinating mathematical concept: Calculating the digits of Pi has been a challenge for mathematicians throughout history, and it continues to be a topic of research and interest today. The quest to find the exact value of Pi has led to the development of new mathematical tools and techniques, and has inspired many people to pursue careers in mathematics and science.
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