We will introduce you some of the most beautiful equations or formulas of all time. These equations may take a very elegant and succint form, or indicate some fundamental relationships between different factors,variables or materials. This list covers a wide range of subjects, such as math (algebra, geometry, calculus), physics, and so on. Some equations, for example most elementary school kids might be familiar with the Pythagorean Theorem. And some college student will finally know the relativity equations in College. You can visit DeepNLP Equation Search Engine and AI Agent Marketplace Search Engine to find the latex code, term explanation of related sources of most comprehensive equation databases and and articles. It covers a wide range of domains, ranging from STEM (Science Technology Engineering and Math) subjects to more quantiative subjects (Finance, Economics) in more advanced level.
If you have your own equations that you would like to bookmark and share, you can also use the Equation Latex Code Bookmark Workspace to Save your equations latex code and related explanations.
Equation
Latex
e^{ix}=\cos x+i\sin x
e^{i\pi} + 1 = 0
Explanation
Euler's formula states any real number x can be expressed as trigonometric functions and the complex exponential function. When x = π, Euler's formula may be rewritten as eiπ + 1 = 0 or eiπ = −1, which is known as Euler's identity.
Reanson of Beautifulness
This Euler's equation elegantly connects five fundamental constants: e, i, \pi, 1, and 0, and showcase the deep relationship between them.
Related
Equation
Latex
a^{2}+b^{2}=c^{2}
Explanation
The Pythagorean Theorem describe some fundamentals of geometrythe relationship between the sides of a right triangle, a and b are the length of two edge of the right triangle and c denotes the length of the triangle diagonal line.
Related
Equation
Latex
\int _{-\infty }^{\infty }e^{-x^{2}}\,dx={\sqrt {\pi }}
Explanation
Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function {\displaystyle f(x)=e^{-x^{2}}} over the entire real line. This integral is significant in probability theory and statistics, particularly in relation to the normal distribution. This integral is significant in probability theory and statistics, particularly in relation to the normal distribution1.
Related
Gaussian Integral
Gaussian Integral Equation
Equation
Latex
\nabla \cdot \vec{D}=\rho_{free} \\\nabla \cdot \vec{B}=0 \\\nabla \times\vec{E}=-\frac{\partial{\vec{B}}}{\partial{t}} \\\nabla \times\vec{H}=\vec{J}_{free}+\frac{\partial{\vec{D}}}{\partial{t}}
Explanation
Related
Wikipedia Maxwell Equations
Maxwell Equations Differential
Maxwell Equations Integral
Equation
Explanation
The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that: The real part of every nontrivial zero of the Riemann zeta function is 1/2.
Latex
\zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+\cdots
\zeta (s)=\prod _{p{\text{ prime}}}{\frac {1}{1-p^{-s}}}={\frac {1}{1-2^{-s}}}\cdot {\frac {1}{1-3^{-s}}}\cdot {\frac {1}{1-5^{-s}}}\cdot {\frac {1}{1-7^{-s}}}\cdots
Riemann zeta function
Euler considered this series in the for real values of s, in conjunction with his solution to the Basel problem. He also proved that it equals the Euler product.
The Riemann hypothesis discusses zeros outside the region of convergence of this series and Euler product. To make sense of the hypothesis, it is necessary to analytically continue the function to obtain a form that is valid for all complex s
Related
Equation
General Relativity describe how energy and mass correlates when moving at high speed (close to the speed of light).
Latex Code
E=mc^{2}
Related
General Relativity