# The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most beautiful equations in mathematics. It serves as the backbone of calculus and links its two main ideas: the concept of integral and the concept of derivative.

In mathematical language, the theorem states that the net change of a smooth and continuous quantity, such as a distance traveled, over a certain time interval is equal to the integral of its rate of change at each specific instance, or in other words, it is equal to the integral of its velocity. This remarkable theorem marks great progress in understanding how quantities can be measured over time – incredibly important in almost every area.

## 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.

## 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…

## 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…

## 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,…