Happy Pi Day!

[Starwalker]

Pi is the ratio of a circle’s circumference to its diameter and its constant for every circle. It’s typically rounded to 3.14, but it’s actually an irrational number, meaning the decimal places continue infinitely without repetition or pattern. This has got me thinking about infinity today. We have only calculated pi to about 50 trillion decimal places. I wonder if pi actually does start repeating at some point. After all, the universe is built upon patterns. Perhaps there’s really no such thing as irrational numbers, just minds incapable of rationalizing them. Have a great pi day everyone!

[Amigoo]

Save some of the treat for Leftover Pi Day (Julian 314, Nov. 9 this year).

As I recall from previous study of Pi, this constant is inherently irrational
(how Pi is calculated relative to increasingly minute slices of the geometry).

My favorite slice of Pi defines the hypotenuse and long side
of a right triangle that squares the circle: 2/sqrt(Pi) =
1.1283791670955125738961589031215..


About Py Day (Pythagorean perspective) ...

c = 2.0 hypotenuse, circle's diameter
b = 1.7724538509055160272981674833411.. sqrt(Pi), long side
a = 0.92650275035220848584275966758914.. sqrt(4-Pi), short side
a^2 + b^2 = c^2 where (4-Pi) + Pi = 4

circle's Area = Pi(r^2) = Pi
Area of square = sqrt(Pi)^2 = Pi

Circular conundrum? ...
Squared circles exist in geometry,
but this can't be proven with math.

Rod

[Starwalker]

Very interesting, Rod!

My favourite thing about pi is how it relates to another irrational constant, e, which is defined as the summation from n=0 to infinity of 1/n!. Which is the limit as n approaches infinity of the expression 1+1/n. It is related to pi, 0, 1, and complex number i through Euler’s identity e^(i*pi)+1=0. The fact that two supposedly irrational numbers can be related in the complex plane blew my mind a little when I learned this in school. My take is that to the One who has infinity at His fingertips, any number can be written as a fraction of two whole numbers.

[Starwalker]

Correction:’imaginary’ number i, not a complex number which has a real and imaginary part. i is the square root of -1. It is not actually possible to take the square root of a negative number, but i is used many practical applications. Much like how our imaginations drive actual creative projects.

[Sandy]

I am sad to say that I don't have a clue what you guys are talking about but good on you, you mathematical wonders...
In all honesty, I told my mom earlier that I was craving a piece of "pi". Okay it was "pie" but close enough, eh?
xxSandy

[Amigoo]

In Cartesian space where D = 2,
Pi can be precisely divided by 2,
gracias a sqrt(2)

See also: http://aitnaru.org/images/Py_Day.pdf

Re: https://www.exploratorium.edu/pi/history-of-pi
"A Brief History of Pi (π)"

"The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.
Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon
inscribed within the circle and the polygon within which the circle was circumscribed."

So, Archimedes actually invented Py Day by using the Pythagorean Theorem?

Note: This later research of Quadrature began by sensing relationship of the square
inscribed within the circle and the square within which the circle was circumscribed
... after all Quadrature is all about squares!

Now, this "impossible" geometry's Lines Of Interest Nested Sentience
in Cartesian space of Quadraturial essence forecasts Pythagorean procreation
annually if not every three trimesters of devoted scholarship.

Rod

[Starwalker]

Sandy, your post gave me a chuckle. Did you get a piece of pie yesterday? I have a great appreciation for the beauty of mathematics, but I know it’s not everyone’s cup of tea.

Thanks for the links, Rod. All your talk on circles and squares makes me think of Circle Square Ranch, an old children’s TV show that taught about God and moral values. Perhaps there was a mathematician behind the scenes there.