Math Facts!
\(0! = 1\)
\(\text{(Factorial of zero is defined as 1)}\)
Math Facts!
\(\text{Order of Operations:}\)
\(\text{Parentheses, Exponents,}\)
\(\text{Multiplication/Division (left to right),}\)
\(\text{Addition/Subtraction (left to right)}\)
Math Facts!
\(A = \frac{1}{2} \times b \times h\)
\(\text{(Area of a triangle formula)}\)
Math Facts!
\(2 \text{ is the only even prime number}\)
\(\text{(All other primes are odd)}\)
Math Facts!
\(F_n = F_{n-1} + F_{n-2}\)
\(\text{(Fibonacci sequence where } F_1=1, F_2=1)\)
Math Facts!
\(X\% \text{ of } Y = Y\% \text{ of } X\)
\(\text{(Percentage calculation trick)}\)
Math Facts!
\(\mathbb{Q} = \left\{\frac{a}{b} \mid a,b \in \mathbb{Z}, b \neq 0\right\}\)
\(\text{(Definition of rational numbers)}\)
Math Facts!
\(\text{1089 Trick: Reverse any 3-digit number,}\)
\(\text{subtract, reverse result, add → always 1089}\)
Math Facts!
\(a^2 + b^2 = c^2\)
\(\text{(Pythagorean theorem for right triangles)}\)
Math Facts!
\(\text{Sum of interior angles}\)
\(\text{in a hexagon } = 720^\circ\)
Math Facts!
\(\text{Four color theorem:}\)
\(\text{Any map can be colored with just 4 colors}\)
\(\text{so no adjacent regions match}\)
Math Facts!
\(1010_2 = 10_{10}\)
\(\text{(Binary to decimal conversion example)}\)
Math Facts!
\(\text{Perfect number: } 28 = 1+2+4+7+14\)
\(\text{(Equals sum of its proper divisors)}\)
Math Facts!
\(\text{Sum of angles in any triangle } = 180^\circ\)
\(\text{(Euclidean geometry fundamental)}\)
Math Facts!
\(A = \pi r^2\)
\(\text{(Area of a circle)}\)
Math Facts!
\(\text{All primes } >3 \text{ can be written as } 6n \pm 1\)
\(\text{(Useful pattern in prime numbers)}\)
Math Facts!
\(e^{i\pi} + 1 = 0\)
\(\text{(Euler's identity connecting 5 fundamental constants)}\)
Math Facts!
\(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\)
\(\text{(Quadratic formula for solving } ax^2+bx+c=0)\)
Math Facts!
\(\phi = \frac{1+\sqrt{5}}{2} \approx 1.618\)
\(\text{(Golden ratio appearing in nature and art)}\)
Math Facts!
\(\text{Pascal's Triangle:}\)
\(\text{Row sums } = 2^n\)
\(\text{(Binomial coefficients pattern)}\)
Math Facts!
\(\text{Birthday Paradox:}\)
\(P(\text{match}) > 50% \text{ with just 23 people}\)
\(\text{(Probability surprise)}\)
Math Facts!
\(T_n = \frac{n(n+1)}{2}\)
\(\text{(Triangular numbers formula)}\)
\(\text{(Example: } 1+2+3+4=10)\)
Math Facts!
\(C = \pi d = 2\pi r\)
\(\text{(Circumference of a circle)}\)
Math Facts!
\(\text{Monty Hall Problem:}\)
\(P(\text{win}) = \frac{2}{3} \text{ when switching doors}\)
\(\text{(Counterintuitive probability result)}\)
Math Facts!
\(\text{Roman numerals:}\)
\(\text{IV} = 4, \text{IX} = 9, \text{XL} = 40\)
\(\text{(Subtractive notation principle)}\)
Math Facts!
\(\int x^n dx = \frac{x^{n+1}}{n+1} + C \ (n \neq -1)\)
\(\text{(Power rule of integration)}\)
Math Facts!
\(\frac{d}{dx}x^n = nx^{n-1}\)
\(\text{(Power rule of differentiation)}\)
Math Facts!
\(\log(ab) = \log a + \log b\)
\(\text{(Logarithm product rule)}\)
Math Facts!
\(a_n = a_1 \times r^{n-1}\)
\(\text{(Geometric sequence formula)}\)
Math Facts!
\(V = \frac{1}{3}\pi r^2 h\)
\(\text{(Volume of a circular cone)}\)
Math Facts!
\(\text{Palindrome numbers:}\)
\(121, 1331, 14641 \text{ (also binomial coefficients)}\)
Math Facts!
\(\text{9 times table pattern:}\)
\(09, 18, 27, 36, 45, 54, 63, 72, 81, 90\)
\(\text{(Digits always sum to 9)}\)
Math Facts!
\(i = \sqrt{-1}\)
\(\text{(Imaginary unit, fundamental to complex numbers)}\)
Math Facts!
\(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R\)
\(\text{(Law of Sines, } R \text{=circumradius)}\)
Math Facts!
\(c^2 = a^2 + b^2 - 2ab\cos C\)
\(\text{(Law of Cosines for any triangle)}\)
Math Facts!
\(S_n = \frac{n(n+1)}{2}\)
\(\text{(Sum of first } n \text{ natural numbers)}\)
Math Facts!
\(V = \frac{4}{3}\pi r^3\)
\(\text{(Volume of a sphere)}\)
