I don’t share your sense of finding beauty and mystery in the sequence of pi as “3.14…” I cannot sympathize with the feeling of finding beauty and mystery in the sequence of “3.14…“.
The area of a circle is 3.14 times larger than the area of a square with the radius of the circle as one side.
The circumference of a circle is 3.14 times longer than its diameter.
On the other hand, Using,
The area of a circle is 0.785 times larger than the area of the square circumscribed by the circle.
The length of the circumference of the circle is 0.785 times the length of the circumference of the square circumscribed by the circle.
In the first place, decimal notation is merely a local rule due to the fact that earthlings are ten-fingered creatures. Intelligent beings with 16 fingers naturally do not use decimal notation, so a sequence of numbers with pi in decimal notation is not universal. The most universal notation is binary notation. Moreover, when pi is written in binary notation, the sequence of bits is identical because 1/4 is just a 2-bit shift.
Note that the area of a polygon circumscribed by a circle is equal to the length of the perimeter of that polygon. This is beautiful.
from Blind spot card with no picture yet Pi (3.1415926..)
The ratio of the lengths of the perimeters of the circle and the square circumscribed by the circle is 0.79 : 1. The ratio of the areas of the circle and the square circumscribed by the circle is 0.79 : 1.
Instead of this 0.79, we call pi 4 times this number, 3.14.
BELOW_IS_AI_GENERATED
円周率
2023-09-05 00:33
Summary of notes
. A discussion of the beauty and mystery of pi. Pi is expressed as the ratio of the area of a circle to a square whose radius is one side of the circle or the ratio of the length of the circumference of the circle, but this is an earthling’s perspective that relies on decimal notation and is not universal. When compared to a square circumscribed by a circle or when binary notation is used, pi is expressed differently. He also points out the beauty of a polygon circumscribed by a circle, where the area of the polygon is equal to the length of its circumference.
Relation to Fragment
. The note and fragment “Pi is τ” share a discussion of how pi is expressed. The note denies the universality of the decimal notation of pi and points out the advantages of the binary notation. On the other hand, Fragment proposes to express pi as τ. These represent different perspectives on how to express pi.
summary of thoughts
The representation of pi depends on one’s point of view, and its universality is relative. The beauty and mystery of pi depends on the way it is expressed and the perspective from which it is viewed.
Title
. “Representing Pi: Relativity and Universality in Perspective.”
extra info
titles: ["Why pi appears in the sum of the reciprocals of square numbers"], "The graphic grasp of numbers", "Pi is τ", "A cylinder looks like a circle or a square, but it is neither a circle nor a square", "Hatena2013-02-07", "Hatena2009-07-10"]
generated: 2023-09-05 00:33
This page is auto-translated from /nishio/円周率 using DeepL. If you looks something interesting but the auto-translated English is not good enough to understand it, feel free to let me know at @nishio_en. I’m very happy to spread my thought to non-Japanese readers.