Happy Pi Day!

Hey! Happy pi day to all my readers!



Here's something cool:
eiπ = -1                                                                      (by Euler’s identity) 
Taking natural logarithm on both sides,
ln (-1) = iπ
 
Hence, π = ln(-1)/i
 







 
Here’s a simple question for pi day:  What does the series above converge at?
 
Anyways, here’s pi to 30 decimal places: 3.141592653589793238462643383279.

Forgot to post, so just adding a Happy Tau Day Here! - 6/28


Comments

Post a Comment

Popular posts from this blog

101: Everything You Need to Know About Lagrangian Mechanics (Mathematical Physics and Classical Mechanics)

Image
Lagrangian mechanics is a powerful mathematical framework that provides a systematic and elegant approach to understanding the dynamics of physical systems. Developed by Joseph-Louis Lagrange in the late 18th century, it offers an alternative formulation to Newton's laws of motion, providing deeper insights into the fundamental principles governing the behaviour of objects. In this post, we will embark on a comprehensive journey into the realm of Lagrangian mechanics, covering its principles, applications, and significance in the field of physics. Joseph Louis Lagrange Image Credit: Encyclopaedia Britannica The Lagrangian Formulation: At the heart of Lagrangian mechanics lies the concept of the Lagrangian, denoted by L. The Lagrangian is a mathematical function that encapsulates the kinetic and potential energies of a system (KE-PE), providing a comprehensive description of its dynamics. By defining the Lagrangian, we can derive the equations of motion for a system using the princi
Read more

111: Begin the New Year with... an Introduction to the Poincaré Conjecture! (Pure Mathematics)

Image
 Hey! It's been a minute since I wrote one of these, so I'm genuinely glad to be back. Happy New Year! I should be more regular now because I'm done with all university applications and I'm relatively free (as free as you can be by year 12). Today I'll be jabbering on a bit about the Poincaré Conjecture, one of the most special (solved) problems in mathematics. The Poincaré Conjecture Image Credit: Clay Mathematics Institute The Poincaré Conjecture is a fundamental problem in the branch of topology, best known as one of the 7 Millennium Prize Problems of the Clay Mathematics Institute. It was one of the most famous and long-standing unsolved problems in the history of mathematics until it was finally proven in 2003 by the Russian mathematician Grigori Perelman. Perelman's proof was a monumental achievement and earned him the Fields Medal and 1 million US Dollars (from the Clay Mathematics Institute) - both of which he declined (which I'll return to later). H
Read more

110: Everything You Need to Know About the Navier-Stokes Equations (Pure Physics and Applied Mathematics)

Image
In the intricate world of fluid dynamics, where the movement of liquids and gases forms the backdrop of countless natural phenomena, the unsolved Clay Institute Millenium Prize Problem of the Navier-Stokes equations stands as a beacon of understanding. These mathematical expressions encapsulate the intricate forces, pressures, and velocities that orchestrate the motion of fluids. George Gabriel Stokes Image Credit: Clay Mathematics Institute Fluid dynamics is a captivating branch of physics and mathematics that delves into the behaviour of fluids in motion. Whether it's the ocean currents, the streams, or the turbulence in a boiling pot, understanding the principles governing fluid motion requires strong mathematical concepts and physics insights. The Navier-Stokes equations, named in honour of the French engineer Claude-Louis Navier and the Irish mathematician George Gabriel Stokes, are the fundamental equations that explain fluid dynamics. In their general form, they can be expre
Read more