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Pi day is tomorrow! 3.14!
What is your most interesting fact or insight about the number Pi?
What is your most interesting fact or insight about the number Pi?
Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.Greg Bernhardt said:Pi day is tomorrow! 3.14!
What is your most interesting fact or insight about the number Pi?
fresh_42 said:Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.
It had been at the end of a lecture script of Linear Algebra. I just don't remember whether it was at the end of the first semester or at the end of the first year.epenguin said:At what level would one have to be for it to be 'not that complicated'?
Fig Neutron said:"May I have a large container of coffee"
david2 said:There are people who like to recite as many digits as possible.
Current world record:70030(!) digits.
http://pi-world-ranking-list.com/index.php?page=lists&category=pi
Ibix said:To better than 0.5%, a year is ##\pi\times 10^7## seconds.
Even worse - numerologist aliens.Borek said:Aliens!
##\pi = - i \ \ln(-1)## or ##\pi = - 2 \ i \ \ln(i)##fresh_42 said:Beside the fact that ##e^{i\pi}+1=0##, it is that it took so unbelievably long until its transcendence has been proven. I have a vague memory of the proof, and it wasn't that complicated.
On the other hand, two pies are better than one.PeroK said:Changing to ##\tau = 2\pi## would be worthwhile just to highlight the pointlessness of that if nothing else.
Just foundBorek said:[tex]\frac {\pi^2} 6= \sum_N \frac 1 {n^2} = \prod_P(1-\frac 1 {p^2})^{-1}[/tex]
(where P are primes and N are natural numbers)
david2 said:There are people who like to recite as many digits as possible.
Current world record:70030(!) digits.
http://pi-world-ranking-list.com/index.php?page=lists&category=pi
Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##fresh_42 said:Just found
$$\int_0^1 \frac{\log x}{x-1} \,dx = \frac{\pi^2}{6}$$
I don't like this Pythagorean numerology in me, but I can't escape its fascination. What is it with this ##\pi^2/6\,##?
Sure. I just wanted to emphasize the visual beauty of the three different expressions by ##\sum\; , \; \prod\; , \;\int##TeethWhitener said:Expand ##\log(x)## in a Taylor series and integrate to get ##\sum \frac{1}{n^2}##
The most interesting fact about Pi is that it is an irrational number, meaning it cannot be expressed as a finite decimal or fraction. It has infinite digits and has been calculated to over 31 trillion digits.
Pi is important because it is a mathematical constant that is used in many calculations and formulas in mathematics, physics, engineering, and other scientific fields. It is also a fundamental concept in geometry, as it represents the ratio of a circle's circumference to its diameter.
The concept of Pi has been studied and used by many ancient civilizations, including the Egyptians, Babylonians, and Greeks. However, the first calculation of Pi was done by Archimedes of Syracuse in the 3rd century BCE. The symbol "π" was later introduced by mathematician William Jones in 1706.
No, Pi cannot be written as a fraction because it is an irrational number. However, it can be approximated by fractions such as 22/7 or 355/113.
The current world record for calculating Pi is held by physicist Peter Trueb, who calculated Pi to 31 trillion digits in 2020. However, with the help of powerful computers, Pi has been calculated to over 50 trillion digits.