Happy Pi Day

image via Wikipedia
image via Wikipedia

Today is Pi Day.3/14, the first three digits  of the transcendental constant pi.

Here is last year’s post on Pi Day.

π is pretty important in maths and number theory. It’s also used a lot in real life to calculate circumferences, volumes and everything related to circles, wheels and anything circular.

I’m actually more interested in the fact that it’s irrational and transcendental, meaning that there is no repetition in the digits, no period to be found, no matter how far you go and that it’s not a solution of a non-zero polynomial equation with rational coefficients. I had a poster in my room before, π @ 1 million digits. I think that I might have posted the 1 million digits in a post last year. It took up a few MBs. Be warned.

Pi at 1 Million

I’ve been meaning to do this for a while. I imagine that 1 million numbers should be easily contained in one single post.

Be warned. π at 1 million decimals in a txt file is about 1MB! Look at π.

On your home computer, you can calculate π at 128 million in about 15 minutes. π at 1 billion takes a bit more than 3 hours. That’s a lot of decimals. For now, 1 million is fine and dandy. I’m actually using the first 2000 decimals in a piece of art that I’m creating.

π at 1 million decimals.

Continue reading “Pi at 1 Million”

Pi @ 1 Million

The irrational and transcendental constant number Pi to 1 million digits.

Pi Day

image via Wikipedia
image via Wikipedia

It’s Pi Day, so happy Pi Day.

Happy π Day!

What’s Pi Day?

Pi Day and Pi Approximation Day are two holidays held to celebrate the mathematical constant π (pi). Pi Day is observed on March 14 (3/14 in American date format), due to π being equal to roughly 3.14. Sometimes it is celebrated on March 14 at 1:59 p.m. (commonly known as Pi Minute). If π is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.). Pi Approximation Day may be observed on any of several dates, most often July 22 (22/7 (European date format) is a popular approximation of π). March 14 also happens to be Albert Einstein‘s birthday.

What’s Pi? It’s one of the most important constants in mathematics.

Binary 11.00100100001111110110…
Decimal 3.14159265358979323846…
Duodecimal 3.184809493B91864…
Hexadecimal 3.243F6A8885A308D31319…
Continued fraction 3 + \cfrac{1}{7 + \cfrac{1}{15 + \cfrac{1}{1 + \cfrac{1}{292 + \ddots}}}}
Note that this continued fraction is not periodic.

Pi or π is one of the most important mathematical constants, approximately equal to 3.14159. It represents the ratio of any circle‘s circumference to its diameter in Euclidean geometry, which is the same as the ratio of a circle’s area to the square of its radius. Many formulas from mathematics, science, and engineering include π.

It is an irrational number, which means that it cannot be expressed as a fraction m/n, where m and n are integers. Consequently its decimal representation never ends or repeats. Beyond being irrational, it is a transcendental number, which means that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) could ever produce it. Throughout the history of mathematics, much effort has been made to determine π more accurately and understand its nature; fascination with the number has even carried over into culture at large.

The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter “περίμετρος”, probably by William Jones in 1706, and popularized by Leonhard Euler some years later. The constant is occasionally also referred to as the circular constant, Archimedes‘ constant (not to be confused with an Archimedes number), or Ludolph‘s number.