Euler–Lagrange Equations

Euler–Lagrange equations have long been considered a pillar of mathematical foundations in the calculus of variations and classical mechanics. They are also often referred to as a beautiful equations derived by Euler and Lagrange. The Euler–Lagrange equations represent a set of second-order ordinary differential equations that identify stationary points of an action functional.

In other words, they allow us to optimize performance by finding the minimum or maximum value of the function on which they act. Understanding this remarkable equation is essential to breakthroughs in engineering and science applications such as robotics, aircraft design, optics, energy optimization, and much more.

The Minimal Surface Equation

The minimal surface equation may be an abstract mathematical concept, but its applications in the real world are clear to see. The phenomena of soap films that form on the…

Callan-Symanzik Equation

Callan-Symanzik Equation provides a mathematically rigorous expression which is essential for understanding why naive expectations of classical behavior do not work in quantum mechanical systems.

1 = 0.999999999….

The idea that one can be expressed as 0.999… followed by an infinite string of nines, is a truly beautiful equation, challenging the boundaries of our understanding and logic. This…

Special Relativity

Albert Einstein's special relativity equation has been a longstanding source of fascination and inspiration for generations. This beautiful equation demonstrates how time and space are relative as they depend on…

Euler’s Characteristic

Euler characteristic is one of mathematics' most efficient and elegant equations and holds great importance for those interested in the anatomy of geometric figures.

Pythagorean Theorem

Pythagorean Theorem is an iconic equation that has been used for millennia, and to this day, it remains the cornerstone of geometry studies. It states that in any right-angled triangle,…

Einstein’s General Relativity Equation

Albert Einstein's most fundamental contribution to science was the development of his general relativity equation. By considering the effects of gravity on mass and space in combination with time, general…