Pi: The Magical Constant in this Changing World
What Pi really is?
Before
knowing our super-hero (‘Pi’) we have to remind the definition of circle. A
Circle is nothing but a two-dimensional closed loop in which the set of all the
points in the 2D plane is equidistant from a reference point called ‘Centre’
[1]. So, the distance from the centre to any point on the circumference of the
circle is constant and the circumference of the circle can only be changed if
we change this constant distance (Radius).
Figure 01: Variability of Circumference with its Radius [Made with Canva]
Then it can
be said that radius is the only variable of circumference of any circle in the
world. From this common sense, let’s form a mathematical syntax:
Circumference α Radius
or, Circumference α Diameter
or, Circumference = Constant × Diameter
Finally, Constant = Circumference/Diameter = Pi = 3.14159……………………. (Infinity)
Now, this ratio of Circumference to
Diameter is a constant and this is known as ‘Pi’,
the irrational number by which many complex scientific phenomena of our nature
can be explained.
"Pi: In Explaining Planetary Motion"
Kepler states his 3rd law
of planetary motion as:
Figure 02: Planetary Motion around the Central massive object
‘Sun’ followed by elliptical path [2]
In this formula of planetary motion, Pi helps to reflect the elliptical path that the rotating planet follows.
Pi: As a Reference term
In case of space curvature:
If,
C/D<pià
Positively Curved Space,
C/D>pi à
Negatively Curved Space
C/D=pi à
Flat Curvature [4]
References
1. BYJU’S. (n.d.). Circles.
Retrieved March 12, 2025, from https://byjus.com/maths/circles/
2. Unknown. (n.d.). Earth
orbit around the Sun [Photograph]. iStockPhoto. Retrieved March 12, 2025,
from https://www.istockphoto.com/
3. Schomburg, J. (n.d.). Lecture
15: Cosmology and the universe. University of Oregon. Retrieved March 12,
2025, from https://pages.uoregon.edu/jschombe/cosmo/lectures/lec15.html
4. Carroll, S. (2010, November 11). The
Pi-on. Preposterous Universe. Retrieved March 12, 2025, from https://www.preposterousuniverse.com/blog/2010/11/11/the-pi-on/
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