# Latex 20 Essential Maths Formula Symbols and How to Write

Mathematical formulas are the backbone of scientific and engineering disciplines, providing concise representations of complex relationships and concepts. LaTeX, a powerful typesetting system, is widely used for writing mathematical documents due to its robust support for mathematical notation. In this blog post, we’ll explore 20 essential mathematical formulas and demonstrate how to write them in LaTeX.

## 20 Maths Formula Symbols in Latex

### 1. Pythagorean Theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse ((c)) is equal to the sum of the squares of the other two sides ((a) and (b)).

a^2 + b^2 = c^2

The quadratic formula provides the solutions for quadratic equations in the form (ax^2 + bx + c = 0).

x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}

### 3. Sum of Arithmetic Series

The sum of the first (n) terms of an arithmetic series.

S_n = \frac{{n}}{2}(a_1 + a_n)

### 4. Sum of Geometric Series

The sum of the first (n) terms of a geometric series.

S_n = \frac{{a_1(1 - r^n)}}{{1 - r}}

### 5. Binomial Theorem

The expansion of the binomial expression ((a + b)^n).

(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

### 6. Area of a Circle

The formula to calculate the area of a circle with radius (r).

A = \pi r^2

### 7. Volume of a Sphere

The formula to calculate the volume of a sphere with radius (r).

V = \frac{{4}}{3} \pi r^3

### 8. Derivative of a Function

The derivative of a function (f(x)) with respect to (x).

f'(x) = \lim_{h \to 0} \frac{{f(x+h) - f(x)}}{{h}}

### 9. Integral of a Function

The integral of a function (f(x)) over the interval ([a, b]).

\int_{a}^{b} f(x) \, dx

### 10. Euler’s Identity

A fundamental equation in mathematics relating exponential, imaginary, and trigonometric functions.

e^{i\pi} + 1 = 0

### 11. Taylor Series Expansion

The expansion of a function (f(x)) around a point (a) into an infinite series.

f(x) = \sum_{n=0}^{\infty} \frac{{f^{(n)}(a)}}{{n!}}(x-a)^n

### 12. Law of Sines

A trigonometric law relating the sides of a triangle to its angles.

\frac{{\sin A}}{{a}} = \frac{{\sin B}}{{b}} = \frac{{\sin C}}{{c}}

### 13. Law of Cosines

A trigonometric law relating the sides and angles of a triangle.

c^2 = a^2 + b^2 - 2ab\cos(C)

### 14. Normal Distribution

The probability density function of a continuous random variable following a normal distribution.

f(x|\mu,\sigma^2) = \frac{1}{{\sigma \sqrt{2\pi}}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}

### 15. Fourier Transform:

A mathematical transform that decomposes a function into its constituent frequencies.

F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \, dt

### 16. Newton’s Second Law of Motion

A fundamental law in classical mechanics relating force, mass, and acceleration.

F = ma

### 17. Ohm’s Law

A fundamental principle in electrical engineering relating voltage, current, and resistance.

V = IR

### 18. Slope-Intercept Form of a Line

The equation of a line in the form (y = mx + b).

y = mx + b

The general form of a quadratic equation.

ax^2 + bx + c = 0

### 20. Probability Mass Function (PMF)

The probability mass function of a discrete random variable.

P(X=x) = f(x)

## Sample Document Code

Below is a LaTeX document containing 20 popular mathematical formulas:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\title{20 Popular Mathematical Formulas}
\author{}
\date{}
\maketitle

\section*{Algebra}

$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$

2. Binomial Theorem:
$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$

\section*{Calculus}

3. Derivative of $$f(x)$$:
$f'(x) = \lim_{{h \to 0}} \frac{{f(x+h) - f(x)}}{h}$

4. Integral of $$f(x)$$:
$\int f(x) \, dx$

\section*{Geometry}

5. Pythagorean Theorem:
$a^2 + b^2 = c^2$

6. Area of a Circle:
$A = \pi r^2$

\section*{Trigonometry}

7. Sine Rule:
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

8. Cosine Rule:
$a^2 = b^2 + c^2 - 2bc \cos A$

\section*{Probability}

9. Probability Density Function (PDF) of Normal Distribution:
$f(x|\mu,\sigma^2) = \frac{1}{{\sigma \sqrt{2\pi}}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

10. Bayes' Theorem:
$P(A|B) = \frac{{P(B|A)P(A)}}{{P(B)}}$

\section*{Statistics}

11. Mean:
$\bar{x} = \frac{{\sum_{i=1}^{n} x_i}}{n}$

12. Standard Deviation:
$\sigma = \sqrt{\frac{{\sum_{i=1}^{n} (x_i - \bar{x})^2}}{n}}$

\section*{Physics}

13. Newton's Second Law:
$F = ma$

14. Einstein's Mass-Energy Equivalence:
$E = mc^2$

\section*{Engineering}

15. Ohm's Law:
$V = IR$

16. Fourier Transform:
$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \, dt$

\section*{Differential Equations}

17. Euler's Identity:
$e^{i\theta} = \cos\theta + i\sin\theta$

18. Laplace Transform:
$F(s) = \mathcal{L}\{f(t)\} = \int_{0}^{\infty} e^{-st} f(t) \, dt$

\section*{Number Theory}

19. Fundamental Theorem of Arithmetic:
$\text{Every integer greater than 1 is either prime or can be expressed as a unique product of primes.}$

\section*{Logic}

20. De Morgan's Laws:
$\lnot (p \land q) \equiv \lnot p \lor \lnot q$
$\lnot (p \lor q) \equiv \lnot p \land \lnot q$

\end{document}

## Conclusion

These 20 mathematical formulas cover a wide range of mathematical concepts and are essential tools in various fields of study. By mastering the writing of these formulas in LaTeX, you can effectively communicate mathematical ideas with clarity and precision in your documents, presentations, and research papers.

Also check: How to Write Plus Minus (±) Symbol in LaTeX

Also check our Latex Table Generator Tool.